#discrete-math | Mathematics | Page 169

weary tiger Apr 8, 2021, 5:19 PM

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beacuse ExEy implies there exists a president and there exists a state s.t.

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but we only want to talk about texas

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i thought that, but texas is in the set of states

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for ex

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Well, yes texas is in the set of states but you see that statement becomes true even if it has nothing to do with texas

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i think he wanted us to use quantification

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yes

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just y?

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maybe ask someone else but I'm fairly sure you can't do ExEy

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ur saying there exists a president and there exists a state such that a pres campaigned in that state and and lost that state

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This is not equivalent to what 21 is saying

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you'd need more relation symbols to say that something is Texas and that something else is Abraham Lincoln

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oh my bad, you're right

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they're not asking you to explicitly state that for texas, but rather form something that would be true if that's true

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in which case that's fine

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I didn't understand the question, sorry! @weary tiger

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prayge this mf owes me points

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Yes, 21 is fine then
22 is fine as well, except maybe 22 is tricking you because some implies more than 1, but if it's not trying to trick you then it should be fine as well

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I think it's safe to assume some means at least one but possibly more

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so ExEy yeah

valid wave Apr 8, 2021, 6:06 PM

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could someone help me out

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this has me so confused

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with modular expressions

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wtf does like a^-1 mean

weary tiger Apr 8, 2021, 6:07 PM

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@valid wave pre-images?

valid wave Apr 8, 2021, 6:08 PM

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for instance solving this

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I know when we have like a congruent to x (mod y)

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it would be a - x = k (y)

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but im so lost when we have like a 3x like here

gritty crescent Apr 8, 2021, 6:16 PM

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This refers to all such x such that 3x-17 is a multiple of 20. One such value is x=19, if I'm not tripping.

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There is a systematic method to solve linear diophantine equations.

valid wave Apr 8, 2021, 6:17 PM

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wait so its still the same idea of saying

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3x - 17

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is mod of etc

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so then how would I show all the solutions

sly ibex Apr 8, 2021, 6:17 PM

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are you danish? @valid wave

gritty crescent Apr 8, 2021, 6:17 PM

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You should look up linear diophantine equations and methods of determining their solutions.

valid wave Apr 8, 2021, 6:18 PM

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this is an intro discrete course

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so i dont think id need such high level theory

gritty crescent Apr 8, 2021, 6:18 PM

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It's a fancy name, nothing high level tbh.

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At least for the linear case.

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I'll dig up some resource.

valid wave Apr 8, 2021, 6:19 PM

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all my question is

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with modular arthemtic

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what is a ^ -1

errant bear Apr 8, 2021, 6:20 PM

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a(a^-1)=1modn

weary tiger Apr 8, 2021, 6:20 PM

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it doesn't always exist

coral raven Apr 8, 2021, 6:20 PM

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if you have x mod n or whatever, then x^-1 is such that x*x^-1 == x^-1*x == 1 mod n, and x^-1 is called the inverse

weary tiger Apr 8, 2021, 6:20 PM

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in this case 3 and 20 are relatively prime so it exists

coral raven Apr 8, 2021, 6:21 PM

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2 == 3^-1 mod 5 bc 2*3 == 6 == 1 mod 5

weary tiger Apr 8, 2021, 6:21 PM

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so you could multiply both sides by the inverse of 3 mod 20

minor lake Apr 8, 2021, 6:22 PM

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You must place in a row the 11 children of the family F and the 4 children of the family B. Knowing that the children of the family B always quarrel, you must separate them by at least one child of the family F.

How many alignments are possible?

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I'd like someone to redirect me based on this chart

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the column on the left is relatively understandable as for the 3 black things

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first one is "Is the order important"
second is "Is there a repetition"
third one is "Do you need to choose a subset of the element amongst all the elements"

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i'm kinda lost

valid wave Apr 8, 2021, 6:54 PM

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got it

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did some practive problems and got it down

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but i got a case where theres no multiplicative inverse

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so im assuming it would be imposiblr

coral raven Apr 8, 2021, 6:54 PM

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yep, that's totally a thing

valid wave Apr 8, 2021, 6:56 PM

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❤️

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Wait maybe im dumb though

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cause 3 of my questions

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dont have inverses

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the 6 , 8 and 8

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dont have inverses

coral raven Apr 8, 2021, 6:58 PM

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uhhh

valid wave Apr 8, 2021, 6:58 PM

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I feel like im doing something wrong

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3 in a row

coral raven Apr 8, 2021, 6:58 PM

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i mean for a

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x = 7 works

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so you're doing something wrong, yeah

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what are you doing

valid wave Apr 8, 2021, 6:59 PM

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wait

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I thought I had to get a sub 0 ^ -1

split haven Apr 8, 2021, 6:59 PM

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in the solution after finding the correct set they check i-vii again, why is that?

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coral raven Apr 8, 2021, 6:59 PM

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valid wave I thought I had to get a sub 0 ^ -1

i don't understand

valid wave Apr 8, 2021, 7:00 PM

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was following this format

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to get a range of values

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I thought that was the process with congruence multiplication

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now im just confused 😦

coral raven Apr 8, 2021, 7:01 PM

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valid wave I thought I had to get a sub 0 ^ -1

oh, a0^-1

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yeah i don't think ppl usually say sub

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they say like a0 or a_0

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tripped me up

valid wave Apr 8, 2021, 7:01 PM

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a_0

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oh ok

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but

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does that mean all 3 arent possible?

coral raven Apr 8, 2021, 7:02 PM

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no

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you're doing something wrong

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because i just showed you a solution for a

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x = 7

valid wave Apr 8, 2021, 7:02 PM

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but that doesnt follow the form of a0^-1

coral raven Apr 8, 2021, 7:02 PM

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??

valid wave Apr 8, 2021, 7:02 PM

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since we cant find an inverse for 6

coral raven Apr 8, 2021, 7:03 PM

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wait ok go back go back go back

valid wave Apr 8, 2021, 7:03 PM

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with z =27

coral raven Apr 8, 2021, 7:03 PM

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what did you get for the solution to 3x == 17 (mod 20)

valid wave Apr 8, 2021, 7:03 PM

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{19 + 20k: k e Z}

coral raven Apr 8, 2021, 7:04 PM

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ok

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just checking, i was worried you had a more fundamental misunderstanding but you don't

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so if you have ax == b (mod c), and a, b and c all have a common factor d

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then you can do like ax/d == b/d (mod c/d) and the solutions will be the same

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more or less

valid wave Apr 8, 2021, 7:06 PM

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hmm

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but wouldnt that only give me 1 case

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sorry I have pea brain

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PepoG

coral raven Apr 8, 2021, 7:07 PM

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no, i think it's a valid thing

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question

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that said i don't understand it

valid wave Apr 8, 2021, 7:09 PM

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im saying

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if all my other solutions have ranges

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how would I get a range for this question

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when 6 doesnt have an multplicative inverse

coral raven Apr 8, 2021, 7:09 PM

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well the new equation is still a modular thing

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which will have a range when you solve it

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so you can just multiply those solutions back again, sorta?

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look

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just trying it helps in this situation i think

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6x == 15 (mod 27)

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if we turn that into

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2x == 5 (mod 9)

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then

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...?

minor lake Apr 8, 2021, 7:10 PM

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minor lake

nvm goti t

valid wave Apr 8, 2021, 7:11 PM

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a0^-1 = 5

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x 0 = 7

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7 + 9k

coral raven Apr 8, 2021, 7:11 PM

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not quite

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the solution is correct, but

coral raven Apr 8, 2021, 7:11 PM

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valid wave a0^-1 = 5

this is wrong

valid wave Apr 8, 2021, 7:11 PM

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how so

coral raven Apr 8, 2021, 7:12 PM

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x = a^-1 * b

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but it's like a = 2, b = 5?

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wait

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wait

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i'm a fool ignore me

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yes

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ok

valid wave Apr 8, 2021, 7:12 PM

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hehe

coral raven Apr 8, 2021, 7:12 PM

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ok so you have 7 + 9k solves the new equation

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so it turns out that 7 + 27k solves the old equation

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but!

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14 + 27k also solves it

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wait

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no it doesn't

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it's 16

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right

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that makes more sense

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because 16 = 7 + 9

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yes

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ok so 7 + 27k solves the new equation, but 16 + 27k and 25 + 27k also solve it

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do you sorta see that that works, even if not how

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because if you keep adding 9 then it's just 34 which is just 7 mod 27

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so as x == 7 mod 9, x == 7, 16 or 25 mod 27

valid wave Apr 8, 2021, 7:22 PM

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modulo makes me sad 😦

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thanks for all the help

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❤️

coral raven Apr 8, 2021, 7:28 PM

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jesus i've forgotten all my modular arithmetic lmao

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slowly but surely i am becoming the meme of the mathematician who can think in 7 dimensions but can't do sums

gritty crescent Apr 8, 2021, 8:20 PM

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realshit

mint bane Apr 9, 2021, 1:58 AM

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A basket holds a set of balls. Each ball is red, green, or blue. How many balls must there be in the basket in order to guarantee that there are at least 5 balls of the same color? Make sure to explain your answer. is this just 15...?

coral raven Apr 9, 2021, 1:59 AM

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nah, 13

mint bane Apr 9, 2021, 1:59 AM

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why

coral raven Apr 9, 2021, 2:00 AM

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4+4+4 is the max without 5 of the same colour

mint bane Apr 9, 2021, 2:00 AM

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"coloUr"

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lol that makes sense tho ty

coral raven Apr 9, 2021, 2:01 AM

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what is the language we are speaking? english

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what am i? english

mint bane Apr 9, 2021, 2:02 AM

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no youre british

coral raven Apr 9, 2021, 2:02 AM

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therefore mine is the opinion which matters, colonial heathen

mint bane Apr 9, 2021, 2:02 AM

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big difference

coral raven Apr 9, 2021, 2:02 AM

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literally in england rn lmao

mint bane Apr 9, 2021, 2:02 AM

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i cant read

mint bane Apr 9, 2021, 3:20 AM

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A person’s birth date consists of the month, day, and year in which that person was born.The domain for a relation R is a set of people. No two people in the group have the same birth date.A person x is related to person y under the relation if x’s birth date is earlier than y’s birth date. Is this relation partial order? Is it strict order? Is it total order? Justify your answers to each

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this is reflexive right

last timber Apr 9, 2021, 3:22 AM

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why it is reflexive?

mint bane Apr 9, 2021, 3:22 AM

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person A shares birthday with themself?

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i think..?

last timber Apr 9, 2021, 3:23 AM

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person x is related to person y under the relation if x’s birth date is earlier than y’s birth date.

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so xRx iff x's birthday date is earlier that x's birthday date...

mint bane Apr 9, 2021, 3:23 AM

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oh wow

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im tired....

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${$ (1, 4), (4, 1), (1, 1), (2, 2), (3, 3), (4, 4) $}$

vital dewBOT Apr 9, 2021, 3:33 AM

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nitezba

mint bane Apr 9, 2021, 3:33 AM

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is this transitive, and if so how

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i like to think of transitivity visually but i dont see it here

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or does (1,4),(4,4),(4,1) make it transitive

gritty crescent Apr 9, 2021, 7:53 AM

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It does seem to be transitive.

weary tiger Apr 9, 2021, 9:07 AM

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oof why if ac congruent bc modm then not necessarly a congruent b mod m

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I don't understand why

flat harness Apr 9, 2021, 9:12 AM

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c may not be invertible mod m

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like if c is zero

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ac=bc mod m always

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c being "zero" just means c is a multiple of m

stray reef Apr 9, 2021, 10:22 AM

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@weary tiger would you like a counterexample?

neon fulcrum Apr 9, 2021, 4:16 PM

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how can I solve 9^203 mod 10 without a calculator?

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all I got so far is = 9^200 * 9^3

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didn't get much easier at all

near prawn Apr 9, 2021, 4:24 PM

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try looking at the last digit

neon fulcrum Apr 9, 2021, 4:27 PM

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3?

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should I rewrite these as powers if 3?

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3^2^200 * 3^2^3?

near prawn Apr 9, 2021, 4:34 PM

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whats the last digit of 9^1, 9^2,9^3...

neon fulcrum Apr 9, 2021, 4:34 PM

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no idea

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that question makes no sense to me

near prawn Apr 9, 2021, 4:35 PM

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9^2 is 81

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last digit is 1

neon fulcrum Apr 9, 2021, 4:35 PM

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ok

near prawn Apr 9, 2021, 4:35 PM

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try find a pattern there

neon fulcrum Apr 9, 2021, 4:35 PM

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the last digits swaps between 1 and 9

weary tiger Apr 9, 2021, 4:39 PM

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What is 9 mod 10?

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And do you know any property about multiplication and the modulo relation?

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if you can answer those two questions you probably can solve your problem.

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just testing some values and it seeming to swap between 1 and 9 is not a proof

neon fulcrum Apr 9, 2021, 4:45 PM

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9 % 10 is 9

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also I not proving anything

weary tiger Apr 9, 2021, 4:47 PM

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yea 9 mod 10 is 9 but uh

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-1 mod 10 is also 9

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and (-1)^n is easy to compute...

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@weary tiger interesting song

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what song

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in ur status

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aw i was reading that

mental thicket Apr 9, 2021, 5:01 PM

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ah sorry lol, I found something that would help answering it. So I was going to try and solve it with that first. I'll post again if you want

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I think I can use Pigeonhole Principle

weary tiger Apr 9, 2021, 5:02 PM

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yea i was thinking that

patent bay Apr 9, 2021, 5:02 PM

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consider the parities of each co-ordinate

weary tiger Apr 9, 2021, 5:02 PM

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pidgeonhole and parity

weary tiger Apr 9, 2021, 5:38 PM

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stray reef <@456226577798135808> would you like a counterexample?

no like is there some kind of intuition behind it?

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I mean sure give me a counter example

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@mental thicket

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if two points have first point both odd/even, second point both odd/even, third point both odd/even then the midpoint is an integer

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but there are only 2*2*2 choices 9 points so by php 2 have the same parity for each coordinate hence midpoint is an integer

stray reef Apr 9, 2021, 5:49 PM

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weary tiger no like is there some kind of intuition behind it?

yeah so a simple one would be 6*25 = 14*25 mod 100 but 6 ≠ 14 mod 100

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the intuition is that you can have two nonzero numbers multiply to 0 mod m

broken kiln Apr 9, 2021, 6:25 PM

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What steps would I have to take to solve a problem like this?

stray reef Apr 9, 2021, 6:35 PM

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there are no steps

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well ok like

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both problems are basically just combinatorics problems

broken kiln Apr 9, 2021, 6:40 PM

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so would it be 10C4 and then 10C2? 10C4 because each vertex is composed of 4 numbers? And then to be adjacent you need the intersection of A and B to equal 2?

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OR instead of 10C2, 4C2? Because you are just looking at two of the same digits of a set of 4?

stray reef Apr 9, 2021, 7:11 PM

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there are 10C4 vertices yes but there are way more than 10C2 edges

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if anything there are 1/2 * (10C2)^3 edges

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no wait

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not (10C2)^3 what am i talking abut

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10!/2!^3

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aka 10C2 * 8C2 * 6C2

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each edge is identified by three selections of two points: $A \cap B$, $A \setminus B$ and $B \setminus A$, the latter two (and only them) being interchangeable since we're dealing with an undirected graph --- hence the $1/2$ at the beginning.

vital dewBOT Apr 9, 2021, 7:17 PM

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Ann

plucky thunder Apr 9, 2021, 7:56 PM

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hey i have a question

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if there is a directed loop

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would it be both a degree in and out

weary tiger Apr 9, 2021, 10:07 PM

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Yes

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why x should be in {1 till m-1} ?

coral raven Apr 9, 2021, 10:12 PM

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it should be less than m and greater than 0

weary tiger Apr 9, 2021, 10:12 PM

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why?

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sorry I didn't really understand why

coral raven Apr 9, 2021, 10:13 PM

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well generally when you do something mod m, you get something greater or equal to 0 and less than m

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because intuitively it's basically the remainder when you divide by m

weary tiger Apr 9, 2021, 10:13 PM

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yes true

coral raven Apr 9, 2021, 10:13 PM

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so it's done

weary tiger Apr 9, 2021, 10:13 PM

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but here its saying that a.x mod m =1

coral raven Apr 9, 2021, 10:13 PM

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yes?

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so?

weary tiger Apr 9, 2021, 10:14 PM

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what we said is that 1 <m correct

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but we didn't say anything about x

coral raven Apr 9, 2021, 10:14 PM

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no

weary tiger Apr 9, 2021, 10:14 PM

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because intuitively it's basically the remainder when you divide by m```

coral raven Apr 9, 2021, 10:14 PM

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yes

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something

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anything

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x is mod m

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also

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a is mod m

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everything is mod m

weary tiger Apr 9, 2021, 10:15 PM

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sorry I got confused

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let me tell you my idea

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and then you tell me what to do

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so we said that the remainder of say a mod m= r , is less than m so r<m

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and that's correct I understand that

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so here we are saying a.x mod m= (a modm times x modm ) modm=1

coral raven Apr 9, 2021, 10:16 PM

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sure

weary tiger Apr 9, 2021, 10:17 PM

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ok now how to continue

coral raven Apr 9, 2021, 10:17 PM

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well x mod m is greater or equal to 0

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and less than m

weary tiger Apr 9, 2021, 10:17 PM

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coral raven and less than m

true

coral raven Apr 9, 2021, 10:18 PM

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because anything mod m is greater or equal to 0, and less than m

weary tiger Apr 9, 2021, 10:18 PM

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yep true

coral raven Apr 9, 2021, 10:18 PM

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now all the article says is it can't be 0 specifically

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because a * x = 1, but anything * 0 = 0

weary tiger Apr 9, 2021, 10:18 PM

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ok so here x mod m is less than m

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yes I understand

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but we still haven't concluded that x <m now we concluded that x modm <m

coral raven Apr 9, 2021, 10:19 PM

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oh

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well we define x as being the smallest one

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x = (x mod m)

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we call that the inverse

weary tiger Apr 9, 2021, 10:19 PM

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ah

coral raven Apr 9, 2021, 10:19 PM

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it makes everything simpler

weary tiger Apr 9, 2021, 10:19 PM

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yes x is congruent x mod m (mod m)

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hence we can replace x by x modm

coral raven Apr 9, 2021, 10:20 PM

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uhhh sure

weary tiger Apr 9, 2021, 10:20 PM

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yeah now I understood it

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see it was so abstract at first

weary tiger Apr 10, 2021, 12:01 AM

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Can someone please help me with a question

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If you could dm me, that would be easier

errant bear Apr 10, 2021, 12:04 AM

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no

gritty crescent Apr 10, 2021, 4:12 AM

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weary tiger Can someone please help me with a question

JustAsk

short hamlet Apr 10, 2021, 4:13 AM

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stray reef Apr 10, 2021, 6:18 AM

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@short hamlet do you still need help w/ this?

short hamlet Apr 10, 2021, 6:52 AM

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i got an answer but im not sure on iot

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it

stray reef Apr 10, 2021, 7:25 AM

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okay, can you show your answer?

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and the work that led up to it if possible

urban saddle Apr 10, 2021, 4:03 PM

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Having this sets, how can I calculate the card of (A intersection Bcomplement intersection Ccomplement)?

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nvm

balmy hornet Apr 10, 2021, 4:49 PM

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How many possible sequences of heads and tails are there in k coin flips? How would i show this using bit shifts?

near prawn Apr 10, 2021, 4:51 PM

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bit shifts?

balmy hornet Apr 10, 2021, 4:53 PM

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like i guess you can shift numbers left or right by a certain number of bit

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im very tempted to say 2^k

near prawn Apr 10, 2021, 4:54 PM

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it is 2^k yea

balmy hornet Apr 10, 2021, 4:54 PM

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coin has 2 sides so 50/50 chance

near prawn Apr 10, 2021, 4:54 PM

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i guess you could consider a head as 1 and a tails as 0

balmy hornet Apr 10, 2021, 4:54 PM

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thats true i guess the part that confuses me is why they ask "How many possible sequences" when there is no number of coin flips

near prawn Apr 10, 2021, 4:55 PM

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by sequence they mean like HTTHTHH for eg

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thats a sequence of heads n tails

balmy hornet Apr 10, 2021, 4:55 PM

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ah ok ok thankyou!

balmy hornet Apr 10, 2021, 5:29 PM

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How many bits do we need to represent the hex number 0xDEAD in binary?
would this be 16? i dont think this is correct because i am not including the "0x"

weary tiger Apr 10, 2021, 5:31 PM

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you want to represent the number 0xDEAD in binary not the string "0xDEAD" in binary

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do you know what 0xDEAD means?

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(and technically this depends HOW you represent it. i'm assuming you want to represent it as a base 2 unsigned integer)

balmy hornet Apr 10, 2021, 5:34 PM

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So im going off of my notes which say, "Hex is base 16. There are 16 possible values for each hex digit
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. We can group 4 bits in a binary number into 1 hex digit." So its a shorter way to show binary

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If i converted hex to binary would it be 110111010101101 (which is only 15)

weary tiger Apr 10, 2021, 5:37 PM

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if that is correct then yea, means you can with just 15 binary digits

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0x is not part of the number. it is just used to say that what you are writing is a hexadecimal representation of a number

balmy hornet Apr 10, 2021, 5:41 PM

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okok that makes more sense then. I was questioning if 0x was a part of it. I may need to double check on that binary just in case. I dont know for sure if it is correct

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thank you!

wanton spade Apr 10, 2021, 6:58 PM

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balmy hornet okok that makes more sense then. I was questioning if 0x was a part of it. I may...

yup 0x is for hexadecimal, and 0 is for octal

pliant horizon Apr 10, 2021, 8:55 PM

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could anyone give me a hint as to how to derive that when a constant coefficient linear recurrence relation has a repeated root, you just multiply by n?

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ex. $a_n=4a_{n-1}-4a_{n-2}\implies a_n=c_12^n+c_2n2^n$

vital dewBOT Apr 10, 2021, 8:55 PM

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nix

pliant horizon Apr 10, 2021, 8:56 PM

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i know reduction order from diff eqs but not sure how i could apply that here

dapper hamlet Apr 10, 2021, 10:04 PM

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anyone in here good with sequences willing to get in a voice call and help me learn how to solve sequence problems efficiently? i cant figure them out half the time and the other half of the time i take way too long

near prawn Apr 10, 2021, 10:50 PM

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pliant horizon could anyone give me a hint as to how to derive that when a constant coefficient...

if r is the repeated of the root of the characteristic equation then equating coefficients of t^2-At-B and (t-r)^2 gives you A=2r and B=-r^2, then you could just plug in nr^n and show it satisfies the relation

pliant horizon Apr 10, 2021, 11:39 PM

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near prawn if r is the repeated of the root of the characteristic equation then equating co...

Sure. A verification is easy, but I feel unsatisfied in starting with the answer ahead of time. I'm looking for a derivation

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With that RR if I suppose $a_n=v_nr^n$, then I get
$$v_n=2v_{n-1}-v_{n-2}$$
Which has, again, only one solution of the form $r^n$, being $v_n=1^n$ (which makes sense in context).

vital dewBOT Apr 10, 2021, 11:43 PM

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nix

pliant horizon Apr 10, 2021, 11:44 PM

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But at least with all repeated roots for second order eqs, it can be reduced to this concrete one

unreal stump Apr 11, 2021, 3:52 AM

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pliant horizon i know reduction order from diff eqs but not sure how i could apply that here

See exponential generating functions

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They convert homogeneous linear reccurences into differential equations

naive gulch Apr 11, 2021, 3:58 AM

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Quick Q

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So we introduce x4

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Where x4 can be integers 0-11

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So can I solve the solution normally and then subtract ?

unreal stump Apr 11, 2021, 3:59 AM

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Why subtract

naive gulch Apr 11, 2021, 3:59 AM

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Oh to account for me making an aux. variable?

#

since the aux variable solution =/= the inequality solution?

unreal stump Apr 11, 2021, 4:01 AM

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The set of aux variable solution is same as inequality solutions

naive gulch Apr 11, 2021, 4:02 AM

#

oh

unreal stump Apr 11, 2021, 4:03 AM

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Because that 4th variable is uniquely defined by the first 3 variables

#

So for every solution for original eqn,you get exactly one solution for aux equation

#

And vice versa

naive gulch Apr 11, 2021, 4:04 AM

#

Ooh I kinda see, yeah its dependent. But then if you directly match the solutions, isn't it saying "three buckets may have less than or equal to 11 fish -> four buckets with 11 fish"

#

Is that the wrong analogy?

unreal stump Apr 11, 2021, 4:05 AM

#

naive gulch Ooh I kinda see, yeah its dependent. But then if you directly match the solution...

That analogy works fine

#

I don't see a problem with that

#

Nvm

naive gulch Apr 11, 2021, 4:05 AM

#

Ah okay. shoot then I'm a little stuck?

unreal stump Apr 11, 2021, 4:06 AM

#

You are mapping each case in "three buckets may have <=11 fish" to a case in "4 buckets combined have 11 fish"

#

Not directly

naive gulch Apr 11, 2021, 4:06 AM

#

ooh ok that makes more sense I think

#

thanks!

urban saddle Apr 11, 2021, 9:51 AM

#

I want to find all the equivalence classes for this equivalence relation, but I'm not really sure how

urban saddle Apr 11, 2021, 10:15 AM

#

<@&286206848099549185>

real arrow Apr 11, 2021, 10:15 AM

#

just factor x² - y² = 0

#

then you should see it

proven garnet Apr 11, 2021, 10:18 AM

#

$x$ and $y$ belong to the same equivalence class if and only if $x^2 = y^2$, that is, $(x-y)(x+y) = 0$, that is, $x =y$ or $ - x = y$. So the equivalence class containing $x$, is ${x, -x}$. You can list all the equivalence classes as ${{x,-x } | x \in \mathbb{Z}_{\ge 0} }$

vital dewBOT Apr 11, 2021, 10:18 AM

#

andreO

proven garnet Apr 11, 2021, 10:19 AM

#

note also that for $x =0$, the equivalence class is just ${ 0}$

vital dewBOT Apr 11, 2021, 10:19 AM

#

andreO

modern lava Apr 11, 2021, 10:27 AM

#

a0=2,n≥1
an=a^2n-1

#

can anyone help plz

urban saddle Apr 11, 2021, 10:28 AM

#

proven garnet $x$ and $y$ belong to the same equivalence class if and only if $x^2 = y^2$, tha...

when I solve $(x-y)(x+y) = 0$ what I do is get 2 differents ecuation, $ x - y = 0$ and $x+y = 0$, so my answer is $x = y$ or $x = -y$

vital dewBOT Apr 11, 2021, 10:28 AM

#

Jackieto

urban saddle Apr 11, 2021, 10:28 AM

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is that any different than your answer?

proven garnet Apr 11, 2021, 10:29 AM

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it's the same

urban saddle Apr 11, 2021, 10:29 AM

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alright was making sure, thank you

proven garnet Apr 11, 2021, 10:31 AM

#

modern lava a0=2,n≥1 an=a^2n-1

unclear what you mean by an=a^2n-1

modern lava Apr 11, 2021, 10:31 AM

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SEC

#

modern lava Apr 11, 2021, 10:33 AM

#

proven garnet unclear what you mean by an=a^2n-1

this

proven garnet Apr 11, 2021, 10:38 AM

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Note $a_1 = 2^2$, $a_2 = a_1^2 = (2^2)^2 = 2^4$ and show by induction that $a_n = 2^{2^n}$

vital dewBOT Apr 11, 2021, 10:38 AM

#

andreO

modern lava Apr 11, 2021, 10:40 AM

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if i put the relpace the n to k

#

it shoud work?

#

replace*

proven garnet Apr 11, 2021, 10:40 AM

#

not entirely sure what you mean

modern lava Apr 11, 2021, 10:41 AM

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I just want to know what the formula

proven garnet Apr 11, 2021, 10:43 AM

#

You have the base cases. And now assume $a_n = 2^{2^n}$. Then from $a_{n+1} = a_n^2 = (2^{2^n})^2 = 2^{2^n\cdot 2} = 2^{2^{n+1}}$. So for all $n \in \mathbb{N}$, you have $a_n = 2^{2^n}$

vital dewBOT Apr 11, 2021, 10:43 AM

#

andreO

modern lava Apr 11, 2021, 10:45 AM

#

vital dew **andreO**

why here the $a_1=2^2

#

$a_1=2^2$

vital dewBOT Apr 11, 2021, 10:45 AM

#

jbr22

modern lava Apr 11, 2021, 10:46 AM

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sorry im weak at this

vital dewBOT Apr 11, 2021, 10:47 AM

#

andreO

#

andreO

#

andreO

modern lava Apr 11, 2021, 10:48 AM

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okayy

modern lava Apr 11, 2021, 11:20 AM

#

#

I got here but I can't continue from here can anyone help plz?

half depot Apr 11, 2021, 11:30 AM

#

hi everyone, do you know a good resource on discrete mathematics?

#

be it a book, or a course, i just want it to be easy to understand and explains every topic well.

gritty crescent Apr 11, 2021, 11:38 AM

#

You might want to check out MIT OCW's Discrete Mathematics course.

#

There's a complete set of video lectures available on their YouTube channel as well as their website. The website additionally has lecture notes and problem sets as well.

balmy hornet Apr 11, 2021, 3:01 PM

#

Ok i do not understand my professor's notes to do this when its simple. I cant wrap my head around it. 10 subscript 2 * 8

#

i can make 8 into 2^3?

last timber Apr 11, 2021, 4:33 PM

#

@balmy hornet yes if i inderstand you correctly and 10_2 means binary number you can convert 8 to binary and multiply them or convert 10_2 to dec, multiply by 8 and convert to binary

weary tiger Apr 11, 2021, 4:54 PM

#

there exists a bijection between the k-fold Cartesian product in A and all words in alphabet A of length k, correct?

last timber Apr 11, 2021, 4:57 PM

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yes

weary tiger Apr 11, 2021, 4:58 PM

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Great, was just checking, thanks

sand cipher Apr 11, 2021, 8:08 PM

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help

#

i understand this like 3 days ago when talking abut it in class and now i forgot alr bruh

slow jewel Apr 11, 2021, 8:15 PM

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use the definition

#

sand cipher Apr 11, 2021, 8:32 PM

#

what's that saying is that for all a,b there exist X

#

what does the next 1 says?
functiona=functionb
therefore a=b

#

??

woeful saffron Apr 11, 2021, 9:21 PM

#

hey guys

#

is 9ab + 3 is odd?

last flicker Apr 11, 2021, 9:32 PM

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depends on the value of a and b lol

last flicker Apr 11, 2021, 9:33 PM

#

sand cipher what's that saying is that for all a,b there exist X

for all and and b in X, f(a)=f(b) implies a=b

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X being the domain of f

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so assume 1/(a+1)=1/(b+1) with a and b in [0,inf) and show that does/does not imply a=b

last flicker Apr 11, 2021, 9:41 PM

#

woeful saffron is 9ab + 3 is odd?

like what are a and b? integers? rationals? even numbers?

woeful saffron Apr 11, 2021, 9:52 PM

#

Give the negation of:

a. all worms live in the ground

b. there is at least one pigeon that does not fly

#

any idea?

#

does anyone knows negation???

haughty garden Apr 11, 2021, 10:17 PM

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a) not all worms live in the ground (or there exists one worm that doesn’t live in the ground)
b) there is no pigeon that does not fly

woeful saffron Apr 11, 2021, 10:18 PM

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i dont understand why it has to be nagative?

#

ca you explain me inverse and converse?

woeful saffron Apr 11, 2021, 10:39 PM

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If the battery is charged then the flashlight works

a) give the modus ponens

b) give the modus tollens

nimble elbow Apr 11, 2021, 11:20 PM

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i dont really get generating functions; if i am to find one that gives the ways to add up to a number k ( 3 + 2 + 2 is seperate from 2 + 3 + 2 ), how would i create a function?

#

i was thinking of saying something to add up to 1 and then multiply out but i am unsure if I can do that

weary tiger Apr 12, 2021, 12:51 AM

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im trying to figure out this problem, it says to factor each polynomial by finding the gcf. but i dont quite know what that means, do you factor the problem and then take that and find the gcf? the problem is 3b^5-6b^4+18b

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the carrots are the squared bits

#

gcf = greatest common factor

weary tiger Apr 12, 2021, 2:28 AM

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@haughty garden any idea of where this logic of true and false come from?

nimble elbow Apr 12, 2021, 3:45 PM

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I got a generating function of $$P _{k}(n) = \sum^{n} _{i=0} P _{k-1}(i)$$, I've gotten it added up until $P _{4}(n)$, but don't really get how to go higher. I also got a gamma function representation. Let's say I wanted to go for $P_{11}(n)$, how would I do that?

neon fulcrum Apr 12, 2021, 7:42 PM

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Hello, I did this proof

#

I am not sure if I need to add some words at the bottom

#

is this good enough?

#

#

To be honest, idk really how this proves anything but I know that getting the two sides equal is a good thing

errant bear Apr 12, 2021, 8:58 PM

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how do u go from the first to the second

neon fulcrum Apr 12, 2021, 9:40 PM

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I used the inductive hypotheses

#

errant bear Apr 12, 2021, 10:29 PM

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thats not the inductive hypothesis

naive gulch Apr 13, 2021, 12:23 AM

#

I

#

Any help on this one?

#

Different strings using all the letters total is just n^r = 390625

#

so is it 390625 - only 1 A consecutively - only 2 consecutive As = our answer

coral raven Apr 13, 2021, 12:25 AM

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only 1 A??

#

getting that in itself is awful

naive gulch Apr 13, 2021, 12:30 AM

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sorry I meant cases where there is only an A isolated with no other consecutive As

coral raven Apr 13, 2021, 12:41 AM

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yeah, but again, getting that is just a really annoying way of doing it

#

intuitively?

#

because it feels like you'll need the 2-ways and 3-ways to get that in itself, so it's not even worth it

#

just try thinking about the positions that the block of 3 can be in, directly

naive gulch Apr 13, 2021, 12:51 AM

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Ah gotcha, sorry Im used to looking at these problems via the subtraction method

#

So we have an 8 space string, to fit the 3 A character block

#

repetition is allowed but its a permutation problem because we have to use all the letters right? Can I just use the r-perm formula?

weary tiger Apr 13, 2021, 1:25 AM

#

there are 6 ways to place the A's, and for each of those, the number of ways to place the remaining 5 letters is the same

#

so it really amounts to finding the number of unique ways to permute RRDVK

#

and then multiplying by 6

#

@naive gulch

naive gulch Apr 13, 2021, 1:28 AM

#

ooh

#

thats an interesting way to approach it thanks!

#

That makes sense Botnuke <3

#

ty both let me try that

mint bane Apr 13, 2021, 4:03 AM

#

got that one, am now completely stumped here

Screen_Shot_2021-04-13_at_12.02.51_AM.png

naive marten Apr 13, 2021, 4:04 AM

#

what happens if you try to get the cartesian product of sets x sets within sets

#

so like A x B where A is {1,2} and B is {{0,2},{2,4}}

rain stone Apr 13, 2021, 4:06 AM

#

mint bane got that one, am now completely stumped here

Part (a) or (b)? In either case, do you have an idea of which direction you want to prove?

#

ie do you have an idea of whether the statements are true or false?

mint bane Apr 13, 2021, 4:08 AM

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leaning towards false but just a hunch

#

hadnt thought about cartesian produc54==t

naive saffron Apr 13, 2021, 4:09 AM

#

naive marten so like A x B where A is {1,2} and B is {{0,2},{2,4}}

Well in this case it's exactly what you'll expect, just all pairs of (a,b) such that a is in A and b is in B. So the cartesian product is just (1,{0,2}), (2,{2,4}), (2,{0,2}), (2,{2,4}). Just treat sets as elements too

naive marten Apr 13, 2021, 4:15 AM

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hmmmmm okie ty

#

so a cartesian product always results in a bunch of () bracketed pairs

mint bane Apr 13, 2021, 4:16 AM

#

so wait if im going to disprove, would a counterexample suffice?

rain stone Apr 13, 2021, 4:18 AM

#

mint bane so wait if im going to disprove, would a counterexample suffice?

Yep!

#

but don't just try to blindly guess a counterexample. See if you can articulate why you think it should be false - what your hunch is. If it isn't, a good place to start is to unpack the definition of A - C and B - C; writing out what it actually means might give some insight

mint bane Apr 13, 2021, 4:27 AM

#

ok wait if i subtract a set with extra elements from a set that doesnt have some of those elements it doesnt matter right

#

like {1,2,3} - {3,42,69} = {1,2}

naive saffron Apr 13, 2021, 4:29 AM

#

yes

rain stone Apr 13, 2021, 4:38 AM

#

mint bane ok wait if i subtract a set with extra elements from a set that doesnt have some...

Yep! this statement and your example are both correct

#

and you're definitely thinking in the right direction 😄

mint bane Apr 13, 2021, 4:53 AM

#

so ik part b is true but can it be done w just a direct proof

#

bc reading it out is intuitive enough but that's never enough ofc

rain stone Apr 13, 2021, 4:59 AM

#

Yep! part (b) is true. Start by writing out the definition of A - C and B - C. To show subset, remember you can just show that if x is in A - C, then x is in B - C '

#

do you have an explicit counterexample for part (a) yet?

mint bane Apr 13, 2021, 5:00 AM

#

ye i got that down w help from my gf too, it's basically when C has elements that are in A and B but individually if that makes sense

rain stone Apr 13, 2021, 5:03 AM

#

mint bane ye i got that down w help from my gf too, it's basically when C has elements tha...

yep! that's exactly it

rain stone Apr 13, 2021, 5:04 AM

#

mint bane ok wait if i subtract a set with extra elements from a set that doesnt have some...

that's why I said you were on the right track here - you can take C = A U B, and then A - C and B - C are both empty, so A - C subseteq B - C, no matter what A and B are

rain stone Apr 13, 2021, 5:04 AM

#

rain stone Yep! part (b) is true. Start by writing out the definition of A - C and B - C. T...

so anyways, do this, and remember you are assuming that A subseteq B. The proof here is pretty fast

mint bane Apr 13, 2021, 5:05 AM

#

oh that's a more abstract proof i like that :)

#

merci for the help

rain stone Apr 13, 2021, 5:13 AM

#

mint bane merci for the help

no problem!

#

also I'm not saying "it's a short proof" to make you feel dumb if you don't get it quickly

#

short doesn't mean easy

#

just konw that if you're doing 3 pages of difficult rearrangements or something, you're probably barking up the wrong tree. THere is a relatively succinct argument

mint bane Apr 13, 2021, 5:16 AM

#

Screen_Shot_2021-04-13_at_1.16.32_AM.png

mint bane Apr 13, 2021, 5:16 AM

#

rain stone just konw that if you're doing 3 pages of difficult rearrangements or something,...

succinct but feels incomplete

rain stone Apr 13, 2021, 5:18 AM

#

That is a little incomplete. In particular, you haven't shown the link between
"if x in A then x in B"
and
"if x in A - C then x in B - C"

#

your last two sentences are literally jsut the thing you are trying to prove

mint bane Apr 13, 2021, 5:22 AM

#

lol im tired

#

so wait if x is in A and x is in B, but is not in C, then the subtraction of C from either A or B will leave x in the respective set

rain stone Apr 13, 2021, 5:28 AM

#

mint bane so wait if x is in A and x is in B, but is not in C, then the subtraction of C f...

Yep, exactly! you break into cases

#

or sorry, cases is the wrong word

#

I deleted that message since it was literally teh whole proof haha

rain stone Apr 13, 2021, 5:30 AM

#

mint bane so wait if x is in A and x is in B, but is not in C, then the subtraction of C f...

so yeah, think about x being in A - C. Is x in A? what does that mean about whether or not x is in B? can x be in C if x is in A - C? with that information, what can you conclude about whether or not x is in B - C?

mint bane Apr 13, 2021, 5:31 AM

#

still feels a bit funky

Screen_Shot_2021-04-13_at_1.31.31_AM.png

rain stone Apr 13, 2021, 5:33 AM

#

you have the idea, I think the wording can be cleaned up

#

Talking about the set diference "removing" an element is a little imprecise

mint bane Apr 13, 2021, 5:34 AM

#

exactly my thoughts lol

rain stone Apr 13, 2021, 5:34 AM

#

Instead, literally just look at the definition of A - C and B - C

#

and see if x satisfies that definition (of being in B - C)

mint bane Apr 13, 2021, 5:34 AM

#

oh wait

rain stone Apr 13, 2021, 5:34 AM

#

if it does, you can just write "since x in B and x not in C, by definition x is in B - C"

mint bane Apr 13, 2021, 5:34 AM

#

im overthinking it

rain stone Apr 13, 2021, 5:34 AM

#

yes haha

mint bane Apr 13, 2021, 5:36 AM

#

Screen_Shot_2021-04-13_at_1.36.17_AM.png

#

yee haw, tysm nicholas :)

rain stone Apr 13, 2021, 5:38 AM

#

no worries! I'm very glad this was helpful

uncut matrix Apr 13, 2021, 6:18 AM

#

for set A = {∅, {∅ , {∅ }}}, and set B = {∅ , {∅ }}

why does B ⊆ A = false while B ∈ A = true?

naive saffron Apr 13, 2021, 6:27 AM

#

well ask yourself is every element of B in A

vital dewBOT Apr 13, 2021, 6:28 AM

#

dackid

#

dackid

weary tiger Apr 13, 2021, 11:28 AM

#

Hello, can anyone help with something?

quaint star Apr 13, 2021, 11:31 AM

#

Probably if you say with what

#

But now I've answered two questions. So you've even used up your bonus question quota for the day. Definitely no more help from me.

weary tiger Apr 13, 2021, 11:33 AM

#

got room for 2 more questions? including this one

#

you got any idea what happened here?

#

specifically the inductive step

pale epoch Apr 13, 2021, 11:40 AM

#

what is this notation

#

essentially what you do to construct the powerset of ${a_1, a_2, \dots, a_k}$ is you take every element of the powerset of ${a_1, a_2, \dots, a_{k-1}}$ once "as is" and once with the element $a_k$ added

vital dewBOT Apr 13, 2021, 11:42 AM

#

Lochverstärker

weary tiger Apr 13, 2021, 11:47 AM

#

You mean the notation P?

young carbon Apr 13, 2021, 11:53 AM

#

pale epoch essentially what you do to construct the powerset of $\{a_1, a_2, \dots, a_k\}$ ...

Could you please elaborate?

pale epoch Apr 13, 2021, 11:54 AM

#

not sure how

#

try it yourself

#

write down the powerset of {a_1, a_2}

#

and use that to construct the powerset of {a_1, a_2, a_3}

worthy shard Apr 13, 2021, 12:38 PM

#

#

can anyone solve this?

pale epoch Apr 13, 2021, 12:41 PM

#

try induction

worthy shard Apr 13, 2021, 12:48 PM

#

oki

nimble elbow Apr 13, 2021, 3:14 PM

#

Can someone help me understand a generating function?

unreal stump Apr 13, 2021, 3:15 PM

#

Go ahead

nimble elbow Apr 13, 2021, 3:18 PM

#

Ok so I have the function; $$ P_k(n) = \sum^{n}_{i=0} P_{k-1}(i) $$ and have a gamma function representation, but im confused as to getting P_11(n)

unreal stump Apr 13, 2021, 3:19 PM

#

Ok so I have the function; $ P_k(n) = \sum^{n}{i=0} P{k-1}(i) $ and have a gamma function representation, but im confused as to getting $P_{11}(n)$

nimble elbow Apr 13, 2021, 3:19 PM

#

let me type it out nicer so that you can see it

vital dewBOT Apr 13, 2021, 3:19 PM

#

Buncho Drunk

unreal stump Apr 13, 2021, 3:19 PM

#

This?

nimble elbow Apr 13, 2021, 3:19 PM

#

yea

#

unreal stump Apr 13, 2021, 3:25 PM

#

$P_k(n)$ just looks like ${n+k-1 \choose n}$

vital dewBOT Apr 13, 2021, 3:27 PM

#

Buncho Drunk

nimble elbow Apr 13, 2021, 3:28 PM

#

so would i prove that with induction?

unreal stump Apr 13, 2021, 3:40 PM

#

gamma(n) is defined to be (n-1)!

#

For natural numbers

#

There's nothing to prove

nimble elbow Apr 13, 2021, 3:48 PM

#

oh yea, thanks

minor lake Apr 13, 2021, 4:12 PM

#

I have 4 12-sided dices

#

if they are all different, I can get 12 x 12 x 12 x 12 = 12^4 throws by intuition

#

uh but what is it even like

#

order matters so it can't be a combination

#

elements are distinct so it can be a permutation with repetitions

#

and since I can't encode the result in a set, it must be a n-permutation

#

however I don't know how I could get the same answer using nPr

#

help

weary tiger Apr 13, 2021, 4:21 PM

#

@minor lake Can you you a bit more clear about what the question is?

minor lake Apr 13, 2021, 4:22 PM

#

if they are all different

#

how many results can I get

#

using something like a formula like nPr

weary tiger Apr 13, 2021, 4:22 PM

#

with 4, 12 sided dices?

minor lake Apr 13, 2021, 4:22 PM

#

yes

weary tiger Apr 13, 2021, 4:23 PM

#

Are you throwing them successively ie. one after the other

#

If so then the answer is 12x12x12x12

minor lake Apr 13, 2021, 4:24 PM

#

i know i just said it

weary tiger Apr 13, 2021, 4:24 PM

#

If you are throwing the 4 dice at the same time then the answer is different

minor lake Apr 13, 2021, 4:24 PM

#

id just like to know if there is a way to use a formula or something,

#

im currently using a chart

#

it gives me the stuff to apply depending on the order, whether or not there are repetitions and if I have to choose a subset among all elements

#

and based on if it's yes or no it gives me a definition like n-permutation if there's order or combination if there isn't any

#

nvm i posted in #help-0 ill just c if someone finds something

#

solved

twin badger Apr 13, 2021, 6:07 PM

#

so if I have like a log function that is basically f(x)=logbase b(x-2) the domain would just be (2,infinity) and range would be all real numbers? range would also work as the target for the funtion of the logarithm right?

#

Also isn't a log inherently always going to be a one-to-one and onto function?

unreal stump Apr 13, 2021, 6:19 PM

#

twin badger so if I have like a log function that is basically f(x)=log*base b*(x-2) the dom...

Yes,as long as b is valid

unreal stump Apr 13, 2021, 6:20 PM

#

twin badger Also isn't a log inherently always going to be a one-to-one and onto function?

Yes inverse of f(x)=log_b(x-2) exists(g(x)=b^x+2)

twin badger Apr 13, 2021, 6:23 PM

#

So seeing as both domain and targets are infinite in scope, the size of the function can just be easily assumed to have |a|=|b|

#

but both sets of elements are infinite right? despite the domain starting after 2

unreal stump Apr 13, 2021, 6:23 PM

#

Yes

twin badger Apr 13, 2021, 6:23 PM

#

weird

unreal stump Apr 13, 2021, 6:23 PM

#

2 infinite sets may have different sizes

#

There is no Bijection from N to R

icy radish Apr 14, 2021, 1:07 AM

#

Hi guys, where would I go to get live help for discrete mathematics?

mint bane Apr 14, 2021, 1:29 AM

#

in an undirected graph, if there is an edge between A and B, does {A, B, A} count as a walk that is neither circuit nor cycle?

sly turtle Apr 14, 2021, 3:53 AM

#

p = {(x, [x]) ∈ A × (A/R) : x ∈ A}

What does A/R mean in this?

marble haven Apr 14, 2021, 4:04 AM

#

is R referring to the real numbers?

sly turtle Apr 14, 2021, 4:15 AM

#

no

#

I think this refers to a quotient space in my book

rain stone Apr 14, 2021, 4:15 AM

#

I'm assuming R is an equivalence relation, and you're taking the quotient of A and R

#

the notation [x] usually refers to an equivalence class

#

And that's ust what makes the most sense

sly turtle Apr 14, 2021, 4:17 AM

#

not one-to-one ,and another example that is one-to-one```

yeah that makes sense for the question. my professor very briefly talked about quotient space so I'm a bit confused still on what exactly A/R is

rain stone Apr 14, 2021, 4:19 AM

#

So the idea of an equivalence relation is that you're defining a new notion of "things being the same". That's why the equivalence relation axioms are the rules that a normal "=" sign follows. When you take the quotient of a set and an equivalence relation, you treat all things that are equivalent under that relation as literally being the same object. If you give me an example of an equivalence relation you've seen, I can give a specific example

sly turtle Apr 14, 2021, 4:20 AM

#

so [x] is all the elements of the set that x is in, that relate to x? I'm probably confusing something lol

rain stone Apr 14, 2021, 4:21 AM

#

sly turtle so [x] is all the elements of the set that x is in, that relate to x? I'm probab...

nope, that's exactly it! But we think of [x] being a single object, not the whole set of related objects

sly turtle Apr 14, 2021, 4:21 AM

#

and when we say 'relate' to x, are we talking about equivalence or could it be something else

rain stone Apr 14, 2021, 4:22 AM

#

We're talking specifically under the equivalence relation

sly turtle Apr 14, 2021, 4:23 AM

#

if [x] is a single object isn't x equivalent to [x]

rain stone Apr 14, 2021, 4:23 AM

#

So we treat [x] as a single object, but it is still the set of all things which are equivalent to x under R

#

In particular, [x] isn't any one element of A, it is a set of elements of A; the idea is that when you quotient A by R, you just treat all those elements as the same, so it doesn't matter which one you pick, they're all completely interchangable

sly turtle Apr 14, 2021, 4:25 AM

#

okay I think the [x] part makes sense to me now.

#

The way my book is wording A/R it sounds like the set of all equivalence classes in A?

rain stone Apr 14, 2021, 4:25 AM

#

that's exactly it!

sly turtle Apr 14, 2021, 4:26 AM

#

i can't find an example in my notes to make it a bit more tangible

#

because I think of something that wouldn't be one to one for p: A -> A/R

rain stone Apr 14, 2021, 4:27 AM

#

I can type up a quick example, give me one second

sly turtle Apr 14, 2021, 4:27 AM

#

so p is a function that takes an element of A and spits out the set of everything equivalent to that element?

rain stone Apr 14, 2021, 4:28 AM

#

Yep, which we call the equivalence class of that element

#

does your course use the notation a ~ b for a being related to b under ~, or do you use like R(a, b)?

#

I just wanna type this up in a way that's consistent with what you've seen

sly turtle Apr 14, 2021, 4:29 AM

#

i've seen a few different ways i saw xRy

#

and i saw congruent symbol

rain stone Apr 14, 2021, 4:34 AM

#

for example, consider the equivalence relation R on the integers Z defined by aRb if a - b is even. We have that 2R2, since 2- 2 is even, that 2R6 because 2 - 6 is even, and in general, that if a and b are even, then aRb, since the difference of two even numbers is even.

Similarly, 3R1 since 3 -1 = 2 is even, that 3R3 since 3 - 3 = 0 is even, and in general, if c and d are odd numbers, then cRd

In this case, Z/R is just two equivalence classes; namely, [0] and [1]. The reason is that, since all even numbers are equivalent, [0] = {..., -4, -2, 0, 2, 4, ...} and since all odd numbers are equivalent,
[1] = {... -3, -1, 1, 3, ....}. Notice that [0] = [2] = [4] = [6] = ..., since the set of elements equivalent to 0 is the exact same as the set of elements equivalent to 2, since 2 and 0 are equivalent

What you've done is taken Z, and collapsed it down to the elements that are distinct under R. There are only really two distinct elements - 0 and 1 - since everything is equivalent to either 0 or 1, so in some sense, under R, there are only two elements. Notice that my choice of 0 and 1 isn't special here, I could take 2 and 3, or 4 and 13, or 1283781232 and 1111111111111111. What matters is that everything is either in the equivalence class of even numbers, or the equivalence class of odd numbers, and I'm just denoting those sets in the easiest way possible.

sly turtle Apr 14, 2021, 4:37 AM

#

ah okay yes thats a good example thank you

rain stone Apr 14, 2021, 5:07 AM

#

sly turtle ah okay yes thats a good example thank you

The intuition that I always keep in mind is that A/R is taking A, and then making things that are equivalent under R actually the same object - I know I've said this, but it's a subtle idea, and once you have it this'll become much clearer

icy radish Apr 14, 2021, 5:10 AM

#

Hiya guys, in not sure if I'm using predicate logic correctly. I'm trying to make sure the notation and the usage of contradiction is proper.

icy radish Apr 14, 2021, 6:52 AM

#

._.

#

Did I write something so wrong that people are afraid to tell me or something 😬

weary tiger Apr 14, 2021, 7:21 AM

#

Is anyone in here good with combinatorics?

weary tiger Apr 14, 2021, 8:37 AM

#

I have a problem where i have to combine legos to form cuboids, where no repetion is allowed, what would be the best way? Permutation or Combination formula? But there is a problem though, only cuboids are valid so random mixes like figure (b) in the picture below is not valid, how would i account for that with either of these formulas? Also figure (c) and figure (d) are valid but the same so they are a repetition i guess

#

worthy shard Apr 14, 2021, 10:01 AM

#

how to prove this?

median eagle Apr 14, 2021, 10:10 AM

#

hi

pale epoch Apr 14, 2021, 10:11 AM

#

worthy shard how to prove this?

induction

worthy shard Apr 14, 2021, 10:12 AM

#

it's similar to the one i asked yesterday

#

but i can seem to even get started on this one

pale epoch Apr 14, 2021, 10:12 AM

#

start by verifying it for n = 1

#

then write down the sum up to n in terms of the sum up to n-1

weary tiger Apr 14, 2021, 1:37 PM

#

Can anyone help me find the symmetric closure of a matrix?

mint bane Apr 14, 2021, 3:14 PM

#

#

need help proving this

unreal stump Apr 14, 2021, 3:39 PM

#

Trivial by intuition

opal cedar Apr 14, 2021, 5:20 PM

#

is there a place here to discuss theory of computation?

jolly ridge Apr 14, 2021, 5:26 PM

#

You have two lists A and B.
A is an unsorted list, whereas, B is sorted.
Given ′𝑋′ a number input by the user, you need to determine whether or not 𝑋 is present in A and B.

In how many ways can I do this?

gritty crescent Apr 14, 2021, 5:26 PM

#

#foundations might work, in case you don't get an answer here @opal cedar .

stray reef Apr 14, 2021, 5:27 PM

#

jolly ridge You have two lists A and B. A is an unsorted list, whereas, B is sorted. Given ...

many ways

#

well, at least two i guess

#

if B is sorted you can look for X in it through binary search

opal cedar Apr 14, 2021, 5:27 PM

#

I don't have the "Advanced" role, so I guess I'll try here. I'm trying to convert a CFG to a CNF/GNF CFG then turn it into a DPDA, but I struggle with ensuring it's deterministic.

jolly ridge Apr 14, 2021, 5:27 PM

#

many ways
@stray reef

And another way for B?

stray reef Apr 14, 2021, 5:27 PM

#

@opal cedar advanced is a self-assignable role, just type ,iam adv in #bots

jolly ridge Apr 14, 2021, 5:28 PM

#

And is there only one way for A?
Which one

stray reef Apr 14, 2021, 5:28 PM

#

well you could just search through B the same as A

#

for A you have no option but to just scan through it all

opal cedar Apr 14, 2021, 5:28 PM

#

thank you, I appreciate it

stray reef Apr 14, 2021, 5:28 PM

#

which should make sense since it's not sorted

#

i mean

jolly ridge Apr 14, 2021, 5:28 PM

#

Which way is the best according to you

stray reef Apr 14, 2021, 5:28 PM

#

why according to me

jolly ridge Apr 14, 2021, 5:29 PM

#

I mean generally

#

Like whicj is more efficient

stray reef Apr 14, 2021, 5:29 PM

#

for A, simply going through it element by element is the most efficient you can possibly imagine

#

you can make it WORSE on purpose if you really want to

jolly ridge Apr 14, 2021, 5:29 PM

#

And for B?

stray reef Apr 14, 2021, 5:30 PM

#

for B you could do binary search, or you could do radix search (idk if that's the right name for it, but it's the formal equivalent of looking up a word in a dictionary by matching the first letter, then the second, etc.)

#

idk why you're asking "how many" ways there are to do it tbh that's kind of a weird question to ask

#

you could make a plethora of formally different algorithms for searching in a sorted list

#

are you SURE you're being asked "how many possible algorithms are there to search for x in B"?

#

or is this another mistranslation issue that i'm running up against and which you'll be unable to clarify because of an invisible language barrier

jolly ridge Apr 14, 2021, 5:32 PM

#

Wait I'll show you

#

Screenshot_2021-04-14-23-02-48-517_com.google.android.apps.docs.png

#

@stray reef

stray reef Apr 14, 2021, 5:35 PM

#

You can do this in more than one way

#

so you were not asked to count all the possible ways

#

idk what your teacher means by "work only for A"

#

an algorithm that works on any list whatsoever will also work on B
i can't think of an algorithm that only FAILS on fully sorted lists and works in all other cases

opal cedar Apr 14, 2021, 6:36 PM

#

Nobody seems interested in my PDA question 😆

proven garnet Apr 14, 2021, 7:54 PM

#

worthy shard

Note that $$\frac{1}{(2i-1)(2i+1)} = \frac{1}{2}\left(\frac{1}{2i-1} - \frac{1}{2i+1} \right)$$ Now you have a telescoping sum where consecutive terms cancel out except the first and the last and you're left with $\sum_{i=1}^n \frac{1}{(2i-1)(2i+1)} = \frac{1}{2}\left(1 - \frac{1}{(2n+1)} \right) = \frac{n}{2n+1}$

vital dewBOT Apr 14, 2021, 7:54 PM

#

andreO

minor lake Apr 14, 2021, 8:00 PM

#

Isn't that Dirac

gritty crescent Apr 14, 2021, 8:04 PM

#

opal cedar Nobody seems interested in my PDA question 😆

Someone asked a question in #foundations if you didn't notice.

opaque chasm Apr 14, 2021, 9:18 PM

#

How do we prove Euler’s Theorem holds if G is not connected?

ripe pendant Apr 14, 2021, 10:14 PM

#

is zermelo-fraklin set theory the foundation of mathamatics?

pale epoch Apr 14, 2021, 10:15 PM

#

what do you mean by foundation?

shut fjord Apr 14, 2021, 10:34 PM

#

I can explain this problem to anyone who wishes to help

pallid lintel Apr 15, 2021, 3:12 AM

#

anyone know much about discrete geometry/computational geometry here? I'm trying to pick a topic for undergrad thesis. Anyway, i had a simple question; if i had a simple polygon and shoot a ray from a known vertex to another known vertex, whats the fastest (order) algorithm for finding out which edge it first intersects, if it does intersect one?

shell glacier Apr 15, 2021, 8:08 AM

#

jolly ridge You have two lists A and B. A is an unsorted list, whereas, B is sorted. Given ...

A, do a linear scan, B do a binary search. If it is possible to have A sorted then do that and apply binary search to both 😄

weary tiger Apr 15, 2021, 12:21 PM

#

Suppose I have the linear congruence 5x [congruent] 8 (mod 5) can't I multiply both sides by 5 and then I get 25x [congruent] 40 (mod 5) and since 25 [congruent] 40 (mod 5) cause 5 divides (25-40) then I obtain x [congruent] 1 (mod 5) Why can't I do this ? what's wrong with it ? I don't understand

last timber Apr 15, 2021, 12:30 PM

#

@weary tiger somehow 5x = 8 mod 5 makes no sense

#

because 5x congruent 0 mod 5

weary tiger Apr 15, 2021, 12:31 PM

#

oh sorry it was a random example

#

anyways suppose it was not 5x like suppose 6x

last timber Apr 15, 2021, 12:34 PM

#

well

#

in general suppose you have ax = b mod n congruence

#

provided a and n are relatively prime

#

then there exists inverse of a modulo n, a^(-1)

weary tiger Apr 15, 2021, 12:35 PM

#

if I have a=b mod m and c=d mod m => ac=bd mod m
is the converse true?

last timber Apr 15, 2021, 12:36 PM

#

no

#

a = 0, d = 0 and b, c = 1

weary tiger Apr 15, 2021, 12:37 PM

#

suppose a and d not equal 0

last timber Apr 15, 2021, 12:37 PM

#

a = d, b = c

last timber Apr 15, 2021, 12:38 PM

#

last timber then there exists inverse of a modulo n, a^(-1)

so you multiply the whole equation by this inverse and get
a^(-1)ax = a^(-1)b mod n

#

or in other words x = a^(-1)b mod n

obtuse minnow Apr 15, 2021, 1:09 PM

#

I’m...

#

Krieg your example only works mod 1.

#

Nvm. Poster asked about the converse. My bad.

stray reef Apr 15, 2021, 1:37 PM

#

mod 1 thonk

weary tiger Apr 15, 2021, 2:44 PM

#

Every equation always holds mod 1

weary tiger Apr 15, 2021, 5:27 PM

#

I am currently studying Discrete Math by the book, this is in Fundamentals chapter. I am quite confused about this question.

stray reef Apr 15, 2021, 5:44 PM

#

this isn't a question, unless the actual question said to prove this

#

what are f_A and f_B?

#

indicator functions of A and of B respectively?

thin sierra Apr 15, 2021, 6:00 PM

#

Hi everyone, I need to help about automata theory. I want to CFG rule tool. ( Ex: L(G)={b^n a^m b^n | n>=0, m>=0 ... As an answer S->bSb | A A-> aa|ε}

weary tiger Apr 15, 2021, 6:35 PM

#

is the inverse of a transitive closure always equal itself? For a matrix

mint bane Apr 15, 2021, 7:44 PM

#

can anyone help me with c and d here pls

Screen_Shot_2021-04-15_at_3.44.05_PM.png

#

i think c is 2 * P(7,3) but idk

weary tiger Apr 15, 2021, 8:52 PM

#

mint bane can anyone help me with c and d here pls

Still need help?

#

Could I get help on this problem?

Screen_Shot_2021-04-15_at_3.31.01_PM.png

mint bane Apr 15, 2021, 8:55 PM

#

weary tiger Still need help?

pls

tawdry edge Apr 15, 2021, 9:18 PM

#

Hi

#

How can I prove scalability on modulus arithmetic relations?

#

i.e. a = b (mod m)

#

then ac = bc (mod m)?

#

c being a constant

sleek swallow Apr 15, 2021, 9:19 PM

#

Well, you mean that c is an integer, yea? Just use the definition of mod

tawdry edge Apr 15, 2021, 9:19 PM

#

I did...

#

this is what I got: m | c(a-b)

#

what do I do now?

#

I tried then using the definition of "divides by"

sleek swallow Apr 15, 2021, 9:20 PM

#

a = b (mod m) means that a-b = km for some integer k. So, now:

ac-bc = (a-b)c = kmc

Since c is an integer, m is an integer and k is an integer. Then, now, ac-bc = (kc)m and since kc is an integer, you are done

tawdry edge Apr 15, 2021, 9:21 PM

#

woah, hold up

#

...

#

Dude, my teacher sucks

#

I was never taught this definition and I kept seeing it in wiki pages

#

MY TEACHER SAID modulus is

#

m | (a-b)...

#

wait...

#

if I have mk = ac - bc

#

how did you get c over to mk?

#

that doesn't make sense

sleek swallow Apr 15, 2021, 9:23 PM

#

What do you mean? We have a-b = km for some integer k, yes? Then:

ac-bc = (a-b)c = kmc

I'm just using a simple fact about a-b which I established based on the conditions given

tawdry edge Apr 15, 2021, 9:24 PM

#

No

#

You are to prove ac = bc (mod m)

#

m is already in relation to ac and bc

#

you can't just add c to m...

sleek swallow Apr 15, 2021, 9:25 PM

#

Yes, we are to prove that ac-bc is divisible by m

tawdry edge Apr 15, 2021, 9:25 PM

#

well!

#

it looks likke mk = c(a-b)

sleek swallow Apr 15, 2021, 9:25 PM

#

so, we write an expression for ac-bc

tawdry edge Apr 15, 2021, 9:25 PM

#

not mck = c(a-b)...

sleek swallow Apr 15, 2021, 9:26 PM

#

No. Let $a = b (mod(m))$. Then, $a-b = km$ for some integer $k$. Now, consider $ac-bc$, where $c$ is an integer. Then:

$$ac-bc = (a-b)c = kmc = (kc)m$$

which follows from the regular rules of integer arithmetic. Since $kc$ is an integer, it follows that $ac = bc (mod(m))$.

vital dewBOT Apr 15, 2021, 9:26 PM

#

Abhijeet

sleek swallow Apr 15, 2021, 9:27 PM

#

You just need to use the definition of divisibility

tawdry edge Apr 15, 2021, 9:27 PM

#

dude

#

this is flat out impossible

#

you cannot derive kmc like that hommie

sleek swallow Apr 15, 2021, 9:27 PM

#

Your teacher said that a = b mod(m) is defined as m divides a-b. This is the same thing as saying that a-b = km for some integer k

tawdry edge Apr 15, 2021, 9:27 PM

#

obviously

sleek swallow Apr 15, 2021, 9:27 PM

#

Why?

tawdry edge Apr 15, 2021, 9:27 PM

#

because look

#

giving the definition of modulus, and of divisibility

#

you can only derive the following

#

bc = ac (mod m)

#

bc and ac are values!

#

so

#

m | (ac - bc)!

#

using modulus definition

#

using divisibility definition

#

we get

#

mk = c(a-b) after factoring!

#

you do not get mck

#

I have no idea why you keep stating that!

sleek swallow Apr 15, 2021, 9:29 PM

#

You just said that we have to show that if $a = b mod(m)$, then $ac = bc mod(m)$. Is that what you want to prove?

vital dewBOT Apr 15, 2021, 9:29 PM

#

Abhijeet

sleek swallow Apr 15, 2021, 9:29 PM

#

urh bad latex but the message is clear

tawdry edge Apr 15, 2021, 9:29 PM

#

Yes

sleek swallow Apr 15, 2021, 9:29 PM

#

Then, what I have written above is correct

tawdry edge Apr 15, 2021, 9:29 PM

#

given then

sleek swallow Apr 15, 2021, 9:29 PM

#

Read it again

tawdry edge Apr 15, 2021, 9:29 PM

#

Bro

sleek swallow Apr 15, 2021, 9:29 PM

#

No, look, what part of it do you not understand?

#

Like, where is the flaw in the reasoning?

tawdry edge Apr 15, 2021, 9:29 PM

#

well... first off, it seems incredulous then

#

to have a statement

#

that goes

#

$a = b mod(m)$, then $ac = bc mod(m)$

vital dewBOT Apr 15, 2021, 9:30 PM

#

MaggyD

tawdry edge Apr 15, 2021, 9:30 PM

#

wouldn't it be proper to say

#

$a = b mod(m)$, then $ac = bc mod(cm)$

vital dewBOT Apr 15, 2021, 9:30 PM

#

MaggyD

sleek swallow Apr 15, 2021, 9:30 PM

#

But that's trivially true whenever c != 0 .

tawdry edge Apr 15, 2021, 9:30 PM

#

because all of our definitions revolve around m being the modulus applied to the values

#

so its absolutely stupid, FUCKING STUPID

#

I HATE THIS SHIT

sleek swallow Apr 15, 2021, 9:31 PM

#

I mean

#

math doesn't operate on the basis of what you hate or don't hate

#

The proof of your statement has been given above so have a look and tell me if there's any significant flaw that you find

tawdry edge Apr 15, 2021, 9:33 PM

#

ok

#

fine I can prove it lmao

#

your screwed

#

let's define

#

ac and bc as ac = q and bc = z

#

q = z (mod m) cannot equal a = b (mod m)

#

there is no way

#

Bro, the only way your proof works is if you do magic

#

you are adding c to M!

#

WHY WOULD YOU MAKE A PRODUCT OUT OF YOUR MODULUS

sleek swallow Apr 15, 2021, 9:35 PM

#

No one is saying that q = z (mod m) is equal to a = b (mod m)

tawdry edge Apr 15, 2021, 9:35 PM

#

Like the intuition makes no sense bro

sleek swallow Apr 15, 2021, 9:35 PM

#

I did not make a product. I'm just using definitions here

tawdry edge Apr 15, 2021, 9:35 PM

#

Homie

#

no your not

#

your addign c to m out of thin air

#

Prove me then, how my definition

#

given a = b (mod M) then ac = bc (mod m) that

sleek swallow Apr 15, 2021, 9:35 PM

#

You are wasting time

tawdry edge Apr 15, 2021, 9:36 PM

#

m | (a-b) = m | c(a-b)

sleek swallow Apr 15, 2021, 9:36 PM

#

There is no addition of c that is going on in the argument

tawdry edge Apr 15, 2021, 9:36 PM

#

it is not POSSIBLE

#

Period...

#

case in point

#

mk = ac - bc does not equal mk = a - b

#

THAT IS IMPOSSIBLE

#

You cannot be making this point right now dude,

sleek swallow Apr 15, 2021, 9:37 PM

#

No, you are wasting time. Either look at the proof and be specific about whatever flaw you think is present in it or leave the channel and do something more productive.

coral raven Apr 15, 2021, 9:37 PM

#

ok let's start over

#

what's the question?

tawdry edge Apr 15, 2021, 9:37 PM

#

$given a = b mod(m)$, then $ac = bc mod(m)$

vital dewBOT Apr 15, 2021, 9:37 PM

#

MaggyD

coral raven Apr 15, 2021, 9:37 PM

#

prove that?

tawdry edge Apr 15, 2021, 9:37 PM

#

Prove the corollary or whatever

#

prove that they are equal

#

?

sleek swallow Apr 15, 2021, 9:38 PM

#

That's not what's being said

coral raven Apr 15, 2021, 9:38 PM

#

well they're not equivalent

#

i can prove the second part from the first part, sure

sleek swallow Apr 15, 2021, 9:38 PM

#

You are given that a = b (mod m). Then, you need to show that ac = bc (mod m), where a,b,c are integers and m is a nonzero integer.

#

There's no sense of 'equality' here.

tawdry edge Apr 15, 2021, 9:39 PM

#

I don't see how

#

you have the same m...

#

why would you apply c to m?

sleek swallow Apr 15, 2021, 9:39 PM

#

Kaisheng, the proof is above. I've already typed it out and I've been explicit. But this person hasn't looked at it/doesn't want to look at it/isn't telling me what's wrong.

#

What do you mean? We aren't applying c to m at all, whatever that means

tawdry edge Apr 15, 2021, 9:39 PM

#

Dude... I'm asking you to show me HOW youc an apply c to m

#

hommie

coral raven Apr 15, 2021, 9:40 PM

#

ok lemme try

#

say ok after every step if you agree

tawdry edge Apr 15, 2021, 9:40 PM

#

No. Let $a = b (mod(m))$. Then, $a-b = km$ for some integer $k$. Now, consider $ac-bc$, where $c$ is an integer. Then:

$$ac-bc = (a-b)c = kmc = (kc)m$$

which follows from the regular rules of integer arithmetic. Since $kc$ is an integer, it follows that $ac = bc (mod(m))$.

vital dewBOT Apr 15, 2021, 9:40 PM

#

MaggyD

tawdry edge Apr 15, 2021, 9:40 PM

#

Straight from the horses mouth.

coral raven Apr 15, 2021, 9:40 PM

#

stop me if you don't agree

tawdry edge Apr 15, 2021, 9:40 PM

#

You are incredulous

coral raven Apr 15, 2021, 9:40 PM

#

ok so slow down maggy

tawdry edge Apr 15, 2021, 9:40 PM

#

Seriously, it says it right there in your argument! You developed a product out of c and M!

coral raven Apr 15, 2021, 9:40 PM

#

lemme try pls

sleek swallow Apr 15, 2021, 9:40 PM

#

-.-

coral raven Apr 15, 2021, 9:40 PM

#

ok so your problem is

#

where do you get kmc from?

tawdry edge Apr 15, 2021, 9:41 PM

#

God only knows... it was his proof....

coral raven Apr 15, 2021, 9:41 PM

#

is that where you find something wrong

#

bruh

#

no but

#

is that where you're stuck

tawdry edge Apr 15, 2021, 9:41 PM

#

yes

coral raven Apr 15, 2021, 9:41 PM

#

ok

tawdry edge Apr 15, 2021, 9:41 PM

#

where doe she get specifically c on the rhs

coral raven Apr 15, 2021, 9:41 PM

#

so given that you have a - b - km

tawdry edge Apr 15, 2021, 9:41 PM

#

or as a product with m

coral raven Apr 15, 2021, 9:41 PM

#

if you have a - b = km

tawdry edge Apr 15, 2021, 9:41 PM

#

yes

coral raven Apr 15, 2021, 9:42 PM

#

ok

tawdry edge Apr 15, 2021, 9:42 PM

#

following

coral raven Apr 15, 2021, 9:42 PM

#

then you can multiply both sides by c and it's still true

#

so ac - bc = kmc

#

are you ok with this

tawdry edge Apr 15, 2021, 9:42 PM

#

sure

coral raven Apr 15, 2021, 9:42 PM

#

so that's where they get kmc from

#

so are you happy with the proof now?

tawdry edge Apr 15, 2021, 9:43 PM

#

Ok... but this is not proof

coral raven Apr 15, 2021, 9:43 PM

#

why not

tawdry edge Apr 15, 2021, 9:43 PM

#

First off

#

look at our corollary statement...

#

ac = bc (mod) m

#

when we drive the equation from here... we get

#

mk = c(a-b)

sleek swallow Apr 15, 2021, 9:44 PM

#

No

tawdry edge Apr 15, 2021, 9:44 PM

#

which is not what you get in your proof

sleek swallow Apr 15, 2021, 9:44 PM

#

You are supposed to SHOW that ac = bc (mod m)

tawdry edge Apr 15, 2021, 9:44 PM

#

...

sleek swallow Apr 15, 2021, 9:44 PM

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In other words, you are supposed to show that ac-bc = mk', for some integer k'

coral raven Apr 15, 2021, 9:44 PM

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what

tawdry edge Apr 15, 2021, 9:44 PM

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Where does it say that?

coral raven Apr 15, 2021, 9:44 PM

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no everyone stop

sleek swallow Apr 15, 2021, 9:44 PM

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from the fact that a = b (mod(m))

coral raven Apr 15, 2021, 9:44 PM

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i'm so incredibly confused

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wait

tawdry edge Apr 15, 2021, 9:44 PM

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Dude it does not say that...

coral raven Apr 15, 2021, 9:44 PM

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ok maggy lemme go through the whole proof

sleek swallow Apr 15, 2021, 9:45 PM

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vital dew **MaggyD**

This is what you wrote

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This is exactly what you wrote

coral raven Apr 15, 2021, 9:45 PM

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stop

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2. a = b + km
3. a - b = km
4. ac - bc = ckm
5. ac - bc == 0 mod m
6. ac == bc mod m```

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are you okay with this

tawdry edge Apr 15, 2021, 9:46 PM

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no

coral raven Apr 15, 2021, 9:46 PM

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ok

tawdry edge Apr 15, 2021, 9:46 PM

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I give up

coral raven Apr 15, 2021, 9:46 PM

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no

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come back

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which lines do you not agree with

tawdry edge Apr 15, 2021, 9:46 PM

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Can we do another proof that is similar

coral raven Apr 15, 2021, 9:46 PM

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no

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this proof

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tell me what you don't understand about this proof

tawdry edge Apr 15, 2021, 9:47 PM

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Frankly, I'm no fool, I understand the idea

coral raven Apr 15, 2021, 9:47 PM

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ok then why do you not like the proof

tawdry edge Apr 15, 2021, 9:47 PM

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given ac = bc from a = b both (mod m)

coral raven Apr 15, 2021, 9:47 PM

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what

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no

sleek swallow Apr 15, 2021, 9:47 PM

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.......

coral raven Apr 15, 2021, 9:47 PM

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tell me what you don't like about the proof

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which step

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2. a = b + km
3. a - b = km
4. ac - bc = ckm
5. ac - bc == 0 mod m
6. ac == bc mod m```

tawdry edge Apr 15, 2021, 9:47 PM

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4,

coral raven Apr 15, 2021, 9:48 PM

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from 4 to 5?

tawdry edge Apr 15, 2021, 9:48 PM

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3-4

coral raven Apr 15, 2021, 9:48 PM

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ok

tawdry edge Apr 15, 2021, 9:48 PM

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You multiply c to m...

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that is incredulous act

coral raven Apr 15, 2021, 9:48 PM

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so if a - b = km, then it is true that ac - bc = ckm

tawdry edge Apr 15, 2021, 9:48 PM

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c is being applied to a and c in the propositions

coral raven Apr 15, 2021, 9:48 PM

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this is a true statement

tawdry edge Apr 15, 2021, 9:48 PM

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never is m modified

coral raven Apr 15, 2021, 9:48 PM

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this is multiplication

tawdry edge Apr 15, 2021, 9:48 PM

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homie... I know

coral raven Apr 15, 2021, 9:48 PM

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ok, then what's the problem

tawdry edge Apr 15, 2021, 9:48 PM

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but look at the expression

coral raven Apr 15, 2021, 9:48 PM

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why can you not do it

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which expression

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ckm?

tawdry edge Apr 15, 2021, 9:48 PM

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no

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the initial proposition

coral raven Apr 15, 2021, 9:48 PM

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ac - bc?

mint bane Apr 15, 2021, 9:49 PM

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please

coral raven Apr 15, 2021, 9:49 PM

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sorry nitezba come back later

tawdry edge Apr 15, 2021, 9:49 PM

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No. Let $a = b (mod(m))$. Then, $a-b = km$ for some integer $k$. Now, consider $ac-bc$, where $c$ is an integer$

vital dewBOT Apr 15, 2021, 9:49 PM

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MaggyD
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

coral raven Apr 15, 2021, 9:49 PM

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maggy, i don't care about the initial proposition

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you asked about the step between lines 3 and 4

tawdry edge Apr 15, 2021, 9:49 PM

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welp that's what it says homei

coral raven Apr 15, 2021, 9:49 PM

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you asked about the steps between lines 3 and 4

tawdry edge Apr 15, 2021, 9:49 PM

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Dude, I'm done... I got more proofs

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to do

coral raven Apr 15, 2021, 9:49 PM

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do you have an issue there

tawdry edge Apr 15, 2021, 9:49 PM

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and I've spent an hour on this shit

coral raven Apr 15, 2021, 9:49 PM

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do you have an issue there

tawdry edge Apr 15, 2021, 9:50 PM

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I have an issue with the whole statement and how you could possibly apply a constant C to your modulus...

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it is fucking stupid

coral raven Apr 15, 2021, 9:50 PM

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at what point in my proof do i apply c to the modulus

tawdry edge Apr 15, 2021, 9:50 PM

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...

coral raven Apr 15, 2021, 9:50 PM

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2. a = b + km
3. a - b = km
4. ac - bc = ckm
5. ac - bc == 0 mod m
6. ac == bc mod m```

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tell me

tawdry edge Apr 15, 2021, 9:50 PM

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step 4

coral raven Apr 15, 2021, 9:50 PM

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no

tawdry edge Apr 15, 2021, 9:50 PM

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nit wit

coral raven Apr 15, 2021, 9:50 PM

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there is no modulus in line 4

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i did not write a 'mod m'

tawdry edge Apr 15, 2021, 9:50 PM

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yes there is

coral raven Apr 15, 2021, 9:51 PM

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i did not write 'mod m'

tawdry edge Apr 15, 2021, 9:51 PM

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if a - b = km if m | ( a - b) then a = b (mod m)

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m is the modulus