help-0

[alpine sable]

I suspect we do some inclusion exclusion stuff now

[dark granite]

well let's not do that yet because there's other cases to cover, right?

[alpine sable]

ok

Hmm I'm not quite sure how to proceed beyond this point

[dark granite]

so this seems tedious right?

that should clue us on the idea that there's a more straightforward way to do this.

[alpine sable]

Ok

[dark granite]

because those intersections will be crazy, and I don't think your teacher meant for you to do A LOT of PIE unless they really don't like you lol

suppose I have 8 spots in a row.

[alpine sable]

Ok

[dark granite]

we know they're in a row since the shirts are being hanged in the guy's wardrobe.

[alpine sable]

yes

Hmm this is somewhat analogous to row questions where some people refuse to stand next to each other

[dark granite]

yes, but not really since no two people are the same. We count shirts of the same kind as the same

[alpine sable]

thats true

[dark granite]

so if I have the 8 spots as $()()()()()()()()$

[ocean seal]

logician_pdx

[dark granite]

what could go in the left most spot?

[alpine sable]

Any of the 8 shirts

[dark granite]

How bout any of the 4 types

[alpine sable]

Ok

[dark granite]

because shirt 1 might not be different from shirt 2 since they could be of the same kind

[alpine sable]

ok

[dark granite]

so let's say we have now $A()()()()()()()$

[ocean seal]

logician_pdx

[alpine sable]

Sure

[dark granite]

how many things can go in the second spot

[alpine sable]

6 shirts or 3 types

[dark granite]

3types

[alpine sable]

ok

[dark granite]

remember these aren't 8 distinct shirts

[alpine sable]

yep

[dark granite]

So now let's suppose we have $AB()()()()()()$

[ocean seal]

logician_pdx

[dark granite]

how many things can go in the third spot?

[alpine sable]

3 types

[dark granite]

yes

Let's suppose we have $ABC()()()()()$

[ocean seal]

logician_pdx

[alpine sable]

Sure

Though it could be A aswell

[dark granite]

but notice

exactly

[alpine sable]

so theres a set of cases here

[dark granite]

one with A in the third spot and one with A not in the third spot

so how many things can go in the fourth spot?

for this case

[alpine sable]

if you have C

Then you can have A, B or D

so 3

[dark granite]

yea

so suppose we have $ABCD()()()()$

[ocean seal]

logician_pdx

[alpine sable]

what are we doing with the other cases?

if its a or b?

[dark granite]

remember that could've been an A where the D is

yea eventually

[alpine sable]

ok

Next one we have to double up now

[dark granite]

so for the last 4 spots

let's just make sure they don't start with D

[alpine sable]

ok

[dark granite]

so how many ways are there to fill the remaining 4 spots

?

[alpine sable]

if they don't start with D

[dark granite]

yes

exactly

[alpine sable]

then we can do an indirect result

[dark granite]

yup

[alpine sable]

so 4! - 3!

[dark granite]

exactly

[alpine sable]

ok

thats 3 x 3!

so 18

[dark granite]

right good

so for this case what's the total count?

[alpine sable]

What do you want to include?

[dark granite]

wym?

[alpine sable]

i see
4 options (A) x 3 options (B) x 2 options (C) x 2 options (D) x 18

the letters are just what we have chosen

[dark granite]

are you sure that case count isn't 4(3)(3)(3)(18)?

[alpine sable]

Hmm

Thats where we go into the mess of whether we have As and Bs again

I'm not sure how to deal with that

[dark granite]

why do you have 2 options for C

[alpine sable]

I thought that it could be C or D

if we chose not to return to A

[dark granite]

hmm okay, now it seems like we're not counting the same case scenario.

The first thing can be any one of 4 things. The second thing can be any one of 3 things (it can't be the first thing).

[alpine sable]

Ye

[dark granite]

so let's do something clever

Without loss of generality, suppose we are left with the shirts A,B,CC,DD.

we need to place these shirts

[alpine sable]

Sure

[dark granite]

so at this moment I'm think of the sequence AB()()()()()()()

let's count the complement for the remaining spots

assume A and B are fixed

[alpine sable]

by complement, what do you mean?

what are we counting to begin with?

[dark granite]

well so we counted directly at first (for those first two slots in the sequence) now we're going to count indirectly. This means take total arrangements of the things we have left over and then subtract off where some to in the 6 letter sequence are next to each other

so we're going to count the number of such ways to fill the remaining spots

[alpine sable]

Ok

Our restriction is that it can't start with B

then

[dark granite]

it's kind of a hard thing to explain. Are you following what I'm saying tho?

okay good

right

[alpine sable]

ye

We fill the remaining spots with A B CC DD

[dark granite]

how many total ways are there to do that?

there'd be 6!/4 right?

[alpine sable]

yes

6 objects 2 double ups

[dark granite]

yup

now how must those objects be placed so that some two are next to each other

[alpine sable]

ah

its like where cc is next to each other

dd is next to each other

[dark granite]

yes

[alpine sable]

add then take away when both

[dark granite]

exactly

and then don't forget B can't be in front

[alpine sable]

Ok

So our total is 6!/4

and if B can't be in front

[dark granite]

so how many where just one type is next to each other?

[alpine sable]

wait hold on

can we deal with the restriction on b first?

[dark granite]

sure

[alpine sable]

ok

[dark granite]

let's break that up into cases if you want

[alpine sable]

ok

[dark granite]

suppose b is first

[alpine sable]

ok

[dark granite]

for this case

suppose b is the type that's next to each other

[alpine sable]

wait sos i dont get what you mean

[dark granite]

well we need to count when BB happens, when CC happens, when DD, happens, when all of em happen, when BB, CC both happen etc.

[alpine sable]

ok

[dark granite]

so if my 6 letter sequence looks like B()()()()()

[alpine sable]

sure

[dark granite]

how many ways can I fill the remaining spots so that no two of the same type are next to each other?

[alpine sable]

thats tough

[dark granite]

why?

any one of 3 things can go right after B right?

[alpine sable]

right ok

But the problem is that we can do either A or C/D

[dark granite]

but then we deal with the whole A business

right

[alpine sable]

and that breaks it ye

[dark granite]

so can we arrange them all at once? all the remaining 5 at once so that no two of the same kind are next to each other

[alpine sable]

this seems like the original problem again

[dark granite]

kind of, but on a smaller scale

we've helped ourselves by reducing the problem down to 6 letters

[alpine sable]

ok

[dark granite]

I do still agree tho, that's still a pain though

so the last 5 could be placed like CDCDA

or like CDADC

or like

CADCD

or like ACDCD

[alpine sable]

ye

[dark granite]

and that's all of em. We'd multiply each by 2 since the C's and D's can swap

[alpine sable]

Sure

[dark granite]

so when b is fixed at the beginning of the 6 letter sequence, what do we have?

[alpine sable]

When B is fixed

I think those are our 4 cases right

so we multiple by 2

so 8?

wait i think im missing something

[dark granite]

CDCAD also right

?

[alpine sable]

ah yes

Ok 10

[dark granite]

yes. the reasoning there is that A can be in anyone of 5 places, and that completely determines how C and D must be placed. C and D can swap so we multiply by 2

[alpine sable]

yep

thats fine by me

[dark granite]

okay cool. so now what?

[alpine sable]

For when B is not at the front

[dark granite]

okay let's do that

[alpine sable]

Sure

I think we can apply the same value for if A is at the front?

[dark granite]

yeah but B being at the front represented that two B's were together

[alpine sable]

ok

[dark granite]

so if B isn't at the front, what do we do?

[alpine sable]

Hmm

We have 3 options right

[dark granite]

for which spot?

[alpine sable]

for the first spot

[dark granite]

yes

[alpine sable]

A, C,D

[dark granite]

okay, but then you get into some more casework right? so I don't recommend doing that

[alpine sable]

no

hmm

[dark granite]

because if A is first, that'll be different from when C is first. Cuz we only have 1 more A

and more than one C

[alpine sable]

I was thinking

Maybe there was a probabilistic way to do this question

[dark granite]

okay let's hear it!!

is this a question from probability?

or is this from combinatorics?

[alpine sable]

No from combinatorics

[dark granite]

okay

[alpine sable]

But its not like they are mutually exclusive areas

[dark granite]

let's hear your probability approach.

agreed

they are slightly different flavors tho

[alpine sable]

well for any shirt in the row other than the front or back

[dark granite]

you talking the row of 8

or the row of 6?

[alpine sable]

yes

8

[dark granite]

okay, we're starting over

good

[dark granite]

I'm listening

[alpine sable]

it would affect 2/7 of the zones beside it

well ignoring the front or back _ _ _ B _ _ _ _ it directly determines _ B _ ie two spots

oop the underline doesnt work

[dark granite]

yup gotcha. You're thinking about the two neighbors

[alpine sable]

ye

[dark granite]

dope I like this thinking. keep going

[alpine sable]

now i dont know if i should go and find probability of being same type or different

but

i'm leaning towards sametype

[dark granite]

okay, let's do it

[alpine sable]

The ans is 864 by the book btw

But

If it was the same type

1/ 8 of the shirts are placed leaving 1/7 chance it is it ... right?

[dark granite]

right

but that depends

where in the line that first shirt is placed

[alpine sable]

ye its not quite that

ye

[young mantle]

Can someone help me solve due by 12

[alpine sable]

@dark granite i'm so sorry we couldnt come up with an answer but I have to go now.

[young mantle]

Idk where I’m going wrong

[dark granite]

it's all good. I know how to do this with a shit ton of casework...in the meantime I'm going to think of a less tedious way to do this.

[alpine sable]

Thanks

[dark granite]

@alpine sable keep thinking about your probability approach as well, that might lead somewhere or open a new way of thinking that could unlock a more straightforward approach.

[nocturne gazelle]

Please osme help

if i have a grid

of squares

9x9 grid

numbered

---    10
---    20
---    30
       .  
        .
       .```

[dark granite]

This sounds more like a physics problem than a math problem. I recommend going to a physics server with this question as this isn't a physics server.

[dark granite]

what are you asking?

[nocturne gazelle]

im writing it out

[dark granite]

okay

[nocturne gazelle]

if i have that grid of boxes

[native temple]

https://www.codewars.com/kata/55e2adece53b4cdcb900006c

Math behind this?

[nocturne gazelle]

and i want to write a function that takes in two inputs, (x coord and y coord)

[dark granite]

this channel is busy

[nocturne gazelle]

how can i have that function output the index of the box

do u see what ti mean

or should i draw it out

[dark granite]

@nocturne gazelle I recommend taking your question to the #computing-software channel, because this seems more like a programming question.

[native temple]

kinda

it's a math question

[nocturne gazelle]

its both

ive made it a math problem so i can ask here

but yes im applying this to cs

ive been thinkling about this all day and ihave no idea

how i could do this

[dark granite]

okay, yeah I still recommend that channel

[nocturne gazelle]

its pretty dead though 😦

[dark granite]

the people there will likely be able to help you much faster

then tag the helpers

This channel is open for math questions

[nocturne gazelle]

this is a math question

theres no cs in this question lmao

coordinate system and geometry

[flat vale]

Is this the correct use of ⇔?

180-α-β⇔180-(α+β)

[dark granite]

no. There's no truth value on either side of the iff arrows

[alpine sable]

Hello

Channel free?

[dark granite]

no

[flat vale]

what does it mean by true value?

the expr is equivalent tho

[dark granite]

You could say 180-α-β=5⇔180-(α+β)=5

[dark granite]

either side of the if and only if arrow should be a statement that has a truth value

simply taking a difference has no truth value

[flat vale]

hm but α and β represents the same value tho

what about this

[dark granite]

but doing what I did with that equation represents a truth value because either that equation is true or its false

[flat vale]

∠A = 180-α-β
⇔ 180-(α+β)

now is it correct?

[dark granite]

still, simply taking a difference assigns no truth value

[dark granite]

nope

[dark granite]

∠A = 180-α-β ⇔ ∠A=180-(α+β) works tho

[flat vale]

you need the truth value to be a number?

[flat vale]

ah okay

[dark granite]

no

the truth value is T (for true) or F (for false)

[flat vale]

i can't make a new line?

[dark granite]

either that equation is true, or it's false

you can make a new line, that's just generally not how if and only if statements are written

like 5 if and only if 5 makes no sense

[flat vale]

i see

[dark granite]

but 5=3 if and only if 3=5 makes sense

[flat vale]

∠A = 180-α-β ⇔ 180-(α+β)

so like this

[dark granite]

no, look at the right hand side. There's no truth value on the right hand side.

there is on the left, but there needs to also be on the right

[old swan]

Calculate 660.3 m + 66.394 m. Use the correct number of significant digits in the answer.

[flat vale]

ah so i can't just remove the =

[dark granite]

∠A = 180-α-β ⇔ ∠A=180-(α+β) works

[dark granite]

this channel is busy

[old swan]

this assignment is due in 10 mins so idc if the channel is busy

[dark granite]

well you can remove it from one side, just make sure both sides have a truth value

[flat vale]

wait wat

[dark granite]

The channel is busy. Please take your question elsewhere

[old swan]

if you think im going to listen your sadly mistaken

[dark granite]

first off, you want an if only if statement that makes sense. Then you want that is actually true.

[flat vale]

Also should I do this instead of ⇔?

∠A = 180-α-β
= 180-(α+β)

[dark granite]

<@&268886789983436800>

[flat vale]

hm

[dark granite]

see above

[flat vale]

this is correct right?

[dark granite]

yes

much better

the if and only if is implicit

@night geyser I'm referring to @old swan

[night geyser]

it's not the responsibility of other people to make up for your misscheduling. please try and be considerate of others. move to an open channel.

[flat vale]

ye i'm just going to ditch ⇔ for this then

[dark granite]

thank you @night geyser

[ancient bear]

Need I remember these?

quick yes no question sorry for storming in

[night geyser]

the only ones of those i know by memory are the first row, which are just saying that the functions are even/odd

but ask your teacher.

[ancient bear]

I am self studying, I'm in high school, I'll be in calculus 2 in like 3 years

[night geyser]

then no.

[quaint trout]

They're basically the same as the normal trig ones. So if you know those these are easy to remember. I don't memorize identities tho, just remember from using them.

[night geyser]

i have never seen a calculus class that expects students to memorize nontrivial hyperbolic identities

[ancient bear]

Cool! Also hi Luna

[quaint trout]

Hi :)

[old swan]

i didnt miss schedule i just dont understand the god damn problem, maybe actually try to help someone that is stressing out instead of handing them off so you dont have to deal with them

[night geyser]

(and once you learn the exponential formula, theyre easy enough to derive)

not understanding the problem and only thinking to ask for help 10 minutes before it's due seems like a scheduling error to me

¯_(ツ)_/¯

[dawn wraith]

I don’t remember many of these,
but I’ve got to say that they are similar to the normal trig identities

[ancient bear]

well, fam, you're doing an assignment that is due in 10 minutes, this is a great opportunity for you to learn that it's better to do assignments as soon as you're given them

[night geyser]

strong induction is just regular induction with a slight twist on it

i'd certainly recommend you get comfortable with regular induction first

[dark granite]

You're misunderstanding what's going on. We're not just "handing you off" out of the blue. The problem is you came in here so disrespectfully with no consideration for the convo already happening here.

[old swan]

Ive been trying to do this fucking problem for the past 30 mins because i was trying to learn how to do it on my own but now ik why i didnt want to come into these stupid chats

[ancient bear]

He just keeps going lmao!

[quaint trout]

@ancient bear if you do want to memorize, do the first three (reading left to right then down), and the x+y ones. The other ones are just derived using those by making x = y or dividing through by different functions.

[old swan]

im a girl dumbass, have you ever heard of a guy named Cathlene?

[dark granite]

you don't have to come to these chats

[flat vale]

bruh people here r volunteers....

[dark granite]

this still doesn't excuse your behavior

[old swan]

then how tf else am i going to do the damn assignment\

[ancient bear]

Here's a tip, friend. Usually in these discords you want to listen and learn. Leave your ego at the door, take a deep breath, and humble yourself. @old swan

[night geyser]

strong induction problems are basically the same thing as regular induction problems

so you can learn both simultaneously i suppose

[dark granite]

@old swan calling people a dumbass isn't going to help you get help.

[night geyser]

but learning regular induction might help you identify when using stronger phrasing is necessary

depends on the student

[quaint trout]

Girl, your time is running out, how about you stop arguing with people on the internet and just try to follow the server's rules so you can get the help you need?

[night geyser]

i've had some students get it immediately, and other (otherwise competent) students struggle with it for weeks

@old swan to actually answer the question, now that this is more open: when adding or subtracting with significance, you round to the least number of digits after the decimal

660.3 has a single digit after the decimal, while 66.394 has three digits after the decimal

the least of these is the single digit

[old swan]

Ive been doing homework since 5 am, it is currently 12:43 at night where i live, im tired, hungry, and frustrated out of my fucking mind, i dont need random people to tell me to calm down

[night geyser]

so you round your sum to a single digit (after the decimal).

had you asked your question in an open channel rather than bulldozing other people, you wouldve gotten an answer like that immediately

rather than getting in a dumb argument about your assignment being due

[old swan]

everytime i go into these channels they dont tell me the answer they try to explain it in the most complicated way and i never understand it

[dark granite]

and you keep coming back lmao.

[night geyser]

because people want you to learn

rather than just feed you answers

[quaint trout]

And if they just tell you the answer, do you understand then or do you just have an answer with zero understanding?

[ancient bear]

You'll always be frustrated if you expect this to be like chegg

[night geyser]

the goal of this discord is NOT "write this course for me", the goal is "help me learn this mathematics"

[vale wigeon]

they dont tell me the answer
of course they don't, that's just not how this server works.

[old swan]

I ASK FOR AN EXPLANATION AND HOW THEY GOT THE ANSWER GENIUS

[ancient bear]

Oh... okay.

[night geyser]

is my explanation insufficient?

[old swan]

no...

[vale wigeon]

then what's the issue?

nami gave you a satisfactory explanation of how to do your problem, did he not?

[night geyser]

¯_(ツ)_/¯

[old swan]

im dumb as a fucking rock and you think i would understand that?

[night geyser]

sorry that our helpers were trying to help people rather than dropping everything to give you an answer

[vale wigeon]

you just said it was sufficient

which implies that you understood it

[old swan]

when tf did i say it was sufficient

[vale wigeon]

right here

[dark granite]

read before you reply lol

[alpine sable]

@dark granite sorry for pinging, but i was wondering if you saw the DM?

[dark granite]

yes, I saw I'll take a look in a minute. This channel is currently busy, so I'll reply later.

[night geyser]

does this clear it up?

[alpine sable]

thanks

[old swan]

i fucking hate math

[dark granite]

is that a yes or no? to Nami's question

[old swan]

idk

[dark granite]

you don't know if that clears it up?

[vale wigeon]

nami asked you: "does this explanation clear up [the problem]?"

this is a yes/no question

[night geyser]

i really don't know how i can be more explicit without just giving the answer

i kind of already DID give the answer

[old swan]

im trying to understand it ok

[vale wigeon]

and you refuse to answer even that

[sleek elbow]

thats okay

[dark granite]

understand what? the question? or the content of the question?

[vale wigeon]

"give me some time to read through your explanation" is a valid answer

[old swan]

oml just give me a second

[vale wigeon]

but just saying "idk" makes you come across as uncooperative

which nobody likes

[old swan]

STOP FOR A SECOND JUST SOLVE ANOTHER PROBLEM OK JESUS CHRIST

[dark granite]

How do we know you won't barge in again?

[vale wigeon]

there's no need to yell

[dark granite]

what kinda game plan? what is it about?

okay sounds fun!

just great lmao

first you freak out, then you study

[sleek elbow]

✅

[dark granite]

don't freak out for too long tho

okay, then cut straight to studying

no

that's unhealthy

and you'll just be cramming everything

okay. cool story. We're talking about what you're doing before the quiz

methods of proof

fosure

if you don't have the methods of proof down, you're gonna have a hard time proving stuff

so def gotta know strong induction so well you can invoke that method of proof in your sleep

you should know weak induction aka regular induction pretty well too

okay then don't study that

you can study all the topics then

really you have two topics you need to study

strong induction and functions

yea so if you know what injection and surjection is, then those two together give bijection.

composition isn't that hard either, it's just a matter of plugging stuff in and making sure you don't screw up where each element lives (co-domain/domain)

ah, easy

yeah I think you're overthinking this

just relax a bit and cover bijections and strong induction.

because bijections will in turn cover injection and surjection

okay

let's see it

hmmmm. I'd spend more time studying functions than strong induction then

yup I'd still study functions more than strong induction

I can't assure you of such a thing because I don't know exactly where your skill level is at.

I can assure you that you could get a 100%, and I can point you to things that I'd recommend you study more, but ultimately it really depends on how well you already know these topics and that is something only you know.

study functions, then strong induction, then functions again.

that's what I'd do if I were you

take breaks in between

go eat lunch or something doing those breaks

don't stare at your textbooks for too long

no!

lmao jk jk

yes, get some rest

yeah but that won't help you if you accidentally fall asleep during your quiz and miss everything

not in the moment

but later yeah that'd be something you'd laugh about

exactly yea

bottom line. whichever one is going to be covered more on the test, study that more

order doesn't really matter so long as you're taking those breaks

take a break every 20 minutes for about 7 minutes

it is

that's why I said that LMAO

then get tf up and take a damn break

stick to the plan man

aight sounds good

you're welcome.

This channel is open for questions

[signal adder]

Whatever the integers n, p and q, $n^{(p^{q})}=(n^{p})^{q}$

[ocean seal]

Karyan54

[signal adder]

Is this affirmation true ?

I say no because

[pearl marlin]

Try with example

Try 2,1,2

[signal adder]

$(n^{p})^{q}=n^{pq}$

[ocean seal]

Karyan54

[quaint trout]

You are correct

But who says n^(pq) isn't equal to n^(p^q)? It might sometimes be. So it's best to give a specific counterexample to show where it fails

Like for these values of n p and q, this is false

[signal adder]

I get 2 for the 1sr, and 4 for the 2nd

[pearl marlin]

Then equation is wrong

[signal adder]

Oh ok

We can't simplify $n^{(p^{q})}$ ?

[ocean seal]

Karyan54

[pearl marlin]

That is power of p ,so no

First you have to solve the above power

[signal adder]

Ok

Thx for your help @pearl marlin & @quaint trout 👍

[quaint trout]

👍

[cloud rain]

how do I solve it?
x^2 + 5x + 6=0

[pearl marlin]

Try middle term spliting, or you can use quadretic formula

[cloud rain]

ok, I'll use middle term

[ancient magnet]

how did they distribute like that , i dont get it

[alpine sable]

They have just expanded the things

Apply the identity to the numerator of the 2 terms

@ancient magnet

[velvet condor]

maximize $P=a^2+b^2+c^2~in~ 0 \leqslant a,b,c \leqslant 2, a+b+c=3$

[ocean seal]

Minh Baka

[velvet condor]

😛

[ancient magnet]

ohh thnnxx

[ionic jewel]

is this not just 2,1,0

you want the things you square to have the largest value

so 2, then 1

[alpine sable]

A student dinner has 140 students. The ballroom can accomodate up to 49 tables, seating 10 at each. How many different ways can the Graduating Students be seated?

[vague jolt]

Strong induction actually seems pretty straight forward

Instead of proving P(k) => P(k+1) we assume P(k) and use it to prove P(k+1)

If anything, it means a bit easier

[cloud rain]

should I use middle term or quadratic formula for this math:
x^2 + x - 2 = 0

[alpine sable]

Middle term

@cloud rain

-1 + 2

[cloud rain]

ok

could you pls send the work out @alpine sable ?

[alpine sable]

Uhm

Use the basic rules

I already told you what it will expand into

[cloud rain]

ok

[vast bobcat]

help please

[acoustic abyss]

What is 5C)

[glass lichen]

What is x when the perimeter is 30

[acoustic abyss]

its 8

ohh got it tysm

[vague jolt]

I'm a little confused

Isn't an injection when there are values of the codomain that aren't in the range?

And a surjection is when some values in the range are reached twice by different inputs?

[true crystal]

if f(x) = f(y) then x = y that is injection

You inverted

[vague jolt]

Sorry I don't understand

[rigid smelt]

you are mixing up between the two

[true crystal]

an injection is when some values in the range are reached twice by different inputs

[rigid smelt]

no

an injection is when only one input maps into at most one output

or a one-to-one function

[vague jolt]

Yeah

And a surjection is when not every value in the codomain are in the range?

[rigid smelt]

yes, not explicitly but you can say so

[vague jolt]

So for the function f some inputs are mapped to multiple outputs and every value in the codomain is in the range?

[true crystal]

How is this false ?

[rigid smelt]

oh oops you said range, sorry misread

[vague jolt]

Or wait

Is something a surjection when every value in the codomain is in the range?

Or when it is not

[rigid smelt]

oh nvm, what you are trying to say is an output is mapped by two different input?

because if so thats false

[true crystal]

Yeah in this is case it is not an injection

[rigid smelt]

just imagine the word injection as what it really says, a needle shooting in a skin thru only one hole

thats how i usually remember it

[vague jolt]

Injection: one to one, every input has one output
surjection: every element in the range is reached

f is neither because it is not one to one f(-2) = f(2) and not every element in the range is reached?

Is this correct?

[true crystal]

I always found that f(x) = f(y) -> x = y is pretty straightforward

[vague jolt]

Wait what lol

If x = y of course f(x) = f(y)

[true crystal]

That is not the way I wrote it

[vague jolt]

I mean if x = y of course f(x) = f(y)

[true crystal]

Yes but that is not what I said

[vague jolt]

What did u say then

[true crystal]

f(x) = f(y) -> x = y

[vague jolt]

Doesn't -> mean "implies"

[true crystal]

Yes

[rigid smelt]

its only one way

so dont write it backwards

[vague jolt]

Injection: one to one, every input has one output
surjection: every element in the range is reached

f is neither because it is not one to one f(-2) = f(2) and not every element in the range is reached?
Is this correct?

@rigid smelt

[rigid smelt]

yes

[vague jolt]

This is the function so u don't need to scroll up

[rigid smelt]

which is what the picture wrote

[vague jolt]

I have a question though

How exactly am I supposed to know if a value is in both the range and codomain

Oh

Wait

I'm stupid

[rigid smelt]

you just have to start with finding the range...

[vague jolt]

It says R is the range

f: R -> R

[rigid smelt]

the range is not R

[vague jolt]

Huh

[rigid smelt]

thats just a map

[vague jolt]

What is R then

[rigid smelt]

its just a notation saying that the input/domain of X will map onto R

[vague jolt]

Doesn't f: R -> R mean a function where the inputs are any real number and the outputs are any real number

Oh I see

[rigid smelt]

not really

[vague jolt]

So it's saying it will be R

So how would the range be solved exactly

For this function

How would I find the range

[rigid smelt]

well just evaluate the endpoints

[pliant oracle]

in this case it's (hopefully) fairly clear but generally it could be more complicated

[vague jolt]

Isn't it -inf to inf

[pliant oracle]

i mean it says -1 isn't in the range

[rigid smelt]

no

[pliant oracle]

f(x) > 0 for all x

[vague jolt]

It says -1 isn't in the codomain

[rigid smelt]

tho i dont think you need to find the range here

[vague jolt]

-1 is in the range and that's why it isn't surjective

Because -1 is in the range but not the codomain

[pliant oracle]

no

[rigid smelt]

an example say that f(x)=-1 does not have a solution is enough

[vague jolt]

Wdym no

[pliant oracle]

i think you've got range and codomain the wrong way round?

[vague jolt]

Oh yeah mb

I meant

Codomain is -inf to inf

Range is f(x) > 0

How would I solve for codomain is what I meant to ask sorry

[pliant oracle]

the codomain is R, by definition

[vague jolt]

Oh so that is the codomain

Because it says f: R -> R

Right?

[pliant oracle]

ye

[vague jolt]

Okay thanks

So just to confirm one last time

[pliant oracle]

the important thing with surjectiveness is whether the range and codomain coincide

[vague jolt]

Injective: one to one function, every output has only one input
surjective: every value in the codomain is reached. (Codomain = Range)

[pliant oracle]

so here f isn't surjective because there are elements of the codomain (pick any number <= 0) such that they are not in the range

[vague jolt]

Range is always a subset of the codomain

But the codomain is not always a subset of range

When codomain is not a subset of range the function is surjective

Correct?

[pliant oracle]

I wouldn't quite phrase it as 'every output has only one input' but rather 'each value of the range corresponds to only one value in the domain'

i mean typically i'd just write it as 'for all x,y in the domain, f(x) = f(y) => x = y'

[vague jolt]

That kinda confuses me

That basically means

"If f(x) = f(y) then that means x = y"

Right?

[pliant oracle]

yeah

[vague jolt]

OH

Wait

I get it

[pliant oracle]

or equivalently, if x and y are not the same, then f(x) and f(y) are not the same

[vague jolt]

Because it's injective

If the outputs are equal

[pliant oracle]

for different inputs, yeah

[vague jolt]

Then the inputs must be equal because it is one to one

[pliant oracle]

indeed

[vague jolt]

Mmm that makes sense now

[pliant oracle]

:)

[vague jolt]

When I saw that the first time

I was a little confused

Because I thought it was obvious

[pliant oracle]

and also here i would change 'subset of range' to simply 'when codomain and range do not coincide'

[vague jolt]

What does coincide mean?

[pliant oracle]

well as in, are equal

since the range is a subset of codomain, so if the codomain is a subset of the range then they are equal

[vague jolt]

I see

[vale wigeon]

to coincide means to be the same thing

[vague jolt]

I like this discord you guys are really helpful

I wish I joined a long time ago

[sleek elbow]

same here

[pliant oracle]

I'm always terrified talking about definitions in the event i make some dumb mistake lmao

but i hope that helped

[vague jolt]

Sometimes my brain takes a long time to process some things but once it's processed I find myself understanding very well

I just get confused over small things and talking to someone about the topic really helps

[alpine sable]

True

[small holly]

1 degree is = how many minutes?

[pliant oracle]

60 arcminutes

just like with time, a minute being a 60th and a second being a 60th of a minute

[vale wigeon]

yes

[vague jolt]

But it is injective because n^3 has a unique output for every input

And therefore n^3 + 1 will also have a unique output for every input

[pliant oracle]

*injective

[vague jolt]

Yes yes sorry

[pliant oracle]

and also

Ye dw

[vale wigeon]

it takes practice

and a lot of it

[pliant oracle]

Best of luck

[glass lichen]

Composition of functions is just putting 1 function as the input to the other

strictly monotone <=> only strictly inc or strictly dec

yes

if it only does one or the other than it's monotone

No

clearly a function like x^2 is both increasing and decreasing since it has a turning point

not including 0

yes, it's not inc or dec there

it depends on the interval you look at

if you take natural domain then it's not strictly

if you impose a domain restriction then you can make it strictly increasing or decreasing

the domain with no restrictions except what naturally restricts it

yes

since strictly inc and dec is the same requirement for injectivity

however it only applies to functions from R to R

as opposed to general functions

[alpine sable]

hello

can someone explain to me the inequality. i remember doing something like this along time ago... but i wanna see it so i can do it 🙂

he explains it, but he doesnt show it.

im trying to set the limits of x and y

[fluid crown]

(-44720 + 95160i) - (41524 + 1381281i)x + (72500 + 41714i)x^2- (25967 - 61716ix^3 +
(2840 - 4226i) x^4 + (82 + 576i) x^5 -
(28 + 24i) x^6 + x^7=0

what shape is this?

;-;

[alpine sable]

Alright lol.

someone ping me if you can help me. 🙂 no rush.

[smoky harness]

(-44720 + 95160i) - (41524 + 1381281i)x + (72500 + 41714i)x^2- (25967 - 61716ix^3 +
(2840 - 4226i) x^4 + (82 + 576i) x^5 -
(28 + 24i) x^6 + x^7=0

anyone got an idea>

[glass lichen]

to "this"

which part?

[woeful mango]

a - im not sure where to start

[glass lichen]

ok well what's the relationship b/w velocity and position?

[smoky harness]

does anyone know my one

[glass lichen]

it's not yours

it's someone elses

[smoky harness]

its also mine

[woeful mango]

do u mean v=ax+b ?

[glass lichen]

No, I mean the relationship b/w velocity and position in general...

[woeful mango]

uhh idk how to explain it in general terms

[glass lichen]

$\dv{x}{t}=v \ \int v(t)\dd{t}=x(t)+C$

[ocean seal]

Mosh

[alpine sable]

so in that parabolic equation v is x?

[glass lichen]

what??

[alpine sable]

im just trying to understand that problem 😛

that is a an equation with x and y in t

right?

[glass lichen]

Oh you mean your question, you get an ellipse using pythagorean

[smoky harness]

$(-44720 + 95160i) - (41524 + 1381281i)x + (72500 + 41714i)x^2- (25967 - 61716ix^3 +
(2840 - 4226i) x^4 + (82 + 576i) x^5 -
(28 + 24i) x^6 + x^7=0

[glass lichen]

in use.

read the rules if you want help

[alpine sable]

well mine is about trying to understand how the limits are met.

i dont understand the inequality math, i was just looking at misaes question as well

[glass lichen]

$-1\leq \sin(t)\leq 1$

[ocean seal]

Mosh

[glass lichen]

that's just a quotable thing.. since it's the range of sine

[alpine sable]

okay, and since its 3sin it becoes -3<sin>3

[glass lichen]

yes, you multiply through by 3

[alpine sable]

okay i understand now, i just wanted to make sure thank you 🙂

was misaes problem an example like this of a parabolic equation

that has x and y in t?

go ahead fear, im just rambling

[smoky harness]

thanks

(-44720 + 95160i) - (41524 + 1381281i)x + (72500 + 41714i)x^2- (25967 - 61716ix^3 +
(2840 - 4226i) x^4 + (82 + 576i) x^5 -
(28 + 24i) x^6 + x^7=0

shape

i think

[bold token]

I don't really understand differentation and integration VISUALLY. I know differentiate is the rate of change of the curve, while the integration idk

[smoky harness]

wtf

[glass lichen]

definite integrals represent signed area under the curve bounded by the integration axis

[woeful mango]

would that be the rule for a? @glass lichen

[charred hound]

Hi,
https://discordapp.com/channels/268882317391429632/490557019623915520/867591348339867658

[floral jungle]

anyone able to do this?

[alpine sable]

How many numbers are there in total in 6 digit numbers? For example we can have 123456, 213456 , 642472 so how many numbers are there when we scramble them?

[topaz scaffold]

9 possibilities for the first digit

10 possibilities for the other 10 digits

No?

9*10^5 is what I got

900000

Wooooo

[true crystal]

Property of logs addition ?

(and don't forget the condition)

[gaunt roost]

so Log3(8x-2)(x-1)=2

and the 3 is subscript

?

[true crystal]

there are conditions on 8x - 2 and x - 1

what happens if I take x = 0 ?

[gaunt roost]

you can't have negative logs right?

[true crystal]

That is it

[gaunt roost]

so x is greater than 0

[true crystal]

8x -2 > 0 and x - 1 > 0

[gaunt roost]

ok thx

[true crystal]

then you need to get rid of the log3

[gaunt roost]

8x squared - 10x + 2 = 9

[true crystal]

yep

[gaunt roost]

just rewrite in exponential form

from there I got it

7/4

thanks!

[half steppe]

can someone please explain to me how the FFT works? what is meant when someone says that "the FFT takes advantage of the 2pi periodicity of the e function"

[gaunt roost]

it's not 7/4?

[true crystal]

No Sorry I misread the question

[gaunt roost]

so it is 7/4 or did we do the question wrong?

[true crystal]

No we did it right xD it is 7 / 4

[gaunt roost]

ok 🙂

[cloud rain]

4x^2 - 9 = 0
How do I solve it?

[true crystal]

Try factorising it

[cloud rain]

can I get the full solution pls

I'm really stuck

[true crystal]

What have you done this far ?

[cloud rain]

nothing

[true crystal]

I am not going to give you the full solution just like that

[cloud rain]

ok...

do I use the quadratic formula?

[gray isle]

consider the difference of two squares

alternative since there isn't a linear x term,
you could first isolate x^2 and hence determine x from that

quadratic formula would also work but its a bit overkill

[cloud rain]

ok

[sharp barn]

What does the xer mean?

[glass lichen]

x is in R

[sharp barn]

huh?

[glass lichen]

x is a real number

[sharp barn]

alright and e?

r?

[glass lichen]

not an e

$\in$

[ocean seal]

Mosh

[sharp barn]

what does that symbolize

[glass lichen]

IN

[gray isle]

(is) in

element of

[glass lichen]

"x is in R"

[sharp barn]

whats r?

[glass lichen]

Real numbers

like when I said x is a real number

[sharp barn]

oh but in this question does xer matters?

[glass lichen]

yes, it defines what x is

[sharp barn]

the questions only ask for determine which is one one or onemany or many one right?

[glass lichen]

yes

[sharp barn]

then for question 5,76,7,8 why is there x more than 0 or x same 0

[glass lichen]

cause it further restricts what x can take on

[sharp barn]

okay what does the symbol in the diagram of one many above O there is a cross and an underline symbol

what does that mean

[glass lichen]

it just shows that 2 inputs give the same output

it's just a visual aid for the fact x^2 is many to one on R

[sharp barn]

oh okay thanks

[exotic mortar]

Need help please

for part b and c

[glass lichen]

ok well to do c you need to do b

basically you want to find the intersection of mx and the line formed by PQ

that intersection by construction will be Q

[exotic mortar]

how do I go ahead of this

[glass lichen]

well what's the slope of PQ given Q is the closest point to P on the line?

[exotic mortar]

-m

[glass lichen]

no

[exotic mortar]

-1

[devout mantle]

Hello guys

[glass lichen]

not -1

[devout mantle]

I have a maths question

If you do not mind

[glass lichen]

in use.

[devout mantle]

Okay sorry

[exotic mortar]

How do I get it

[glass lichen]

in words what is the slope going to be?

[devout mantle]

So which channel is available ?

[glass lichen]

use common sense @devout mantle

read timestamps...

[devout mantle]

Okay , sorry for being dumb.

[exotic mortar]

-1 divided by slope of line y

[glass lichen]

yes, because PQ is perpendiculur

so the slope of PQ is -1/m

so you can find the equation of the line formed by PQ since you know the slope and the co-ordinates of P

[exotic mortar]

do I use y-y1=m(x-x1)

[glass lichen]

yes

$y-y_1=\frac{-1}{m}(x-x_1)$

[ocean seal]

Mosh

[glass lichen]

cause that's just subbing in the slope of -1/m due to how P was defined

so you need to find the intersection of that and y=mx, so plug in y=mx into that and solve for x to get the x co-ordinate of Q

[exotic mortar]

that gives mx-y1+-1/m (x-x1)

[glass lichen]

yes, which is linear in x

so you can solve for x

[exotic mortar]

but what abt y1

[alpine sable]

how do i solve x^3=27

My Brain is melting

[glass lichen]

it's just a number

[alpine sable]

There are obviously 3 answers

Because the exponent is 3

But i dont understand why i'd have to use the quadratic formula to obtain

[glass lichen]

the question said it'll be in terms of x_1, y_1 and m

[alpine sable]

to obtain 2 of them

[thorn tapir]

only one real root, try to use a^3 - b^3 formula

[glass lichen]

is x in R or C?

[exotic mortar]

is it possible to help on voice im still a bit confused

[glass lichen]

no I dont do vc

[exotic mortar]

oh ok

[glass lichen]

plus it's algebra

[alpine sable]

x^3=27, hint there are 3 answers. you will have to use the quadratic formula for two of them

[thorn tapir]

Factorize man

[alpine sable]

Right

[glass lichen]

yeah, like was suggested already

[alpine sable]

But quadratic formula

Where does that

come into play

[thorn tapir]

a^3 - b^3 = (a - b)(a^2 + ab+b^2)

[glass lichen]

FACTOR IT

[alpine sable]

Ok

Thank you

[river hearth]

help please?

last homework problem and am very stuck

[dawn wraith]

Have you heard of the law of sines?

[dusty viper]

I kinda need help in one part of my hw can someone help?😔

[dawn wraith]

I suppose I can, if @river hearth doesn’t need any more help

[exotic mortar]

use cosine rule

[river hearth]

can you explain?

[dusty viper]

Okay imma wait until this guy is over

So I won’t interrupt

[exotic mortar]

c^2=a^2+b^2-2(a)(b)(cosC)

[dawn wraith]

That’s not possible, you don’t have the angle between the side lengths.

[exotic mortar]

oh yeah nvm

im dumb

[dawn wraith]

Or rather is possible, just doesn’t help

[exotic mortar]

use sine rule

to get the different angles

[dusty viper]

@dawn wraith shall I show you now?

[dawn wraith]

Are you good @river hearth ?

[river hearth]

yeah

[dawn wraith]

Okay, yes.

mpoliou

Shoot

[dusty viper]

So I have this equation which is true for every x possible

But it also needs me to prove that f(x)>0 for every x possible too

[dawn wraith]

Channel is occupied @proven quiver .

Could you please translate the greek?

[dusty viper]

Okay yes

Please wait a second, my English are not that good

[dawn wraith]

Take your time lad

[dusty viper]

You are given this function f:R->R (which means that x ∈ R and f(x) ∈ R) and then they gave us this formula I showed you

And the question is “prove that f(x)>0 , x ∈ R

Sorry it took so long

[dawn wraith]

Hmm

Okay I’ll see what I can do

[dusty viper]

Okay thank you so much^.^

[gaunt roost]

I did A and B, but how would I go about C?

[noble sinew]

You know 12e^x>0 for any x. And you have f(x) and f^3(x) on LHS so if f(x) was negative then since raised to an odd power LHS would be negative

Contradiction so f(x)>0 for any x

[dawn wraith]

Yeah

I was just about type that in

[dusty viper]

Oh, thank you!

[alpine sable]

Hey, If I have to prove that there are infinitely many non prime numbers, I could prove it like this right?

[dawn wraith]

I was only stuck on the f^3(x) part

[dusty viper]

Yeah that’s what made me come here and seek for help

[alpine sable]

How would I prove the same for a prime?

[dawn wraith]

Noted

[noble sinew]

Pretty much same idea

[alpine sable]

I don't get it

I mean

I could add one

And I won't know if it is a prime or not

[noble sinew]

Yes

If prime then done

[alpine sable]

If not then?

[noble sinew]

If not prime then think of prime factorization

[alpine sable]

Ohhh

[noble sinew]

And conclude your original list of primes were not complete

[alpine sable]

Okay

I don't get how can I use prime factorization in this context a small hint would be really appreciated

What I get here is that

[dusty viper]

@noble sinew can I ask what is LHS, because you know, I don’t know English math terms

[dawn wraith]

Left hand side.

[alpine sable]

Left hand side

I got it scape

Prof

[noble sinew]

Well then there would be a prime, q, that divides your product of primes+1

If our list were complete it would be a part of the primes, so a p_i

[alpine sable]

Hey wait

[noble sinew]

So it would divide product of all primes and product of all primes+1

[alpine sable]

Lemme say

What I have to say

[noble sinew]

Oh

[alpine sable]

I didn't read what you said

Now

Lets say there are finitely many primes

[dusty viper]

Oh okay thanks

[alpine sable]

Let p be a number which is a product of all our primes + 1

According to the general theory of arithmetic, every number can be expressed as a product of some primes

But when we divide the number p by one of our finite primes

We get remainder 2

1*

Hence proofed by contradiction

Is it correct?

[noble sinew]

Yessir

[alpine sable]

Thanks

[marsh valley]

If $x^2+bx+9$ has two non-real roots, find all real possible values of $b$. Express your answer in interval notation.

[ocean seal]

BAAPA|INDIAN ELITES

[marsh valley]

how are you supposed to find b?

like I guess b=6 would make it a perfect square, but that would only have 1 root

[indigo jetty]

use the discriminant

[marsh valley]

oh

\sqrt {b^2 - 4ac}

[icy trail]

$\sqrt {b^2 - 4ac}$

[dawn wraith]

$$\sqrt {b^2 - 4ac}$$

[ocean seal]

Hunnydrips

[dawn wraith]

XD

[icy trail]

snap

[marsh valley]

so the discriminant would be $b^2 - 36$

[icy trail]

$\sqrt {b^2 - 4ac} > 0$

[ocean seal]

BAAPA|INDIAN ELITES

querty

[indigo jetty]

u should be forming an inequality involving the discriminant

[icy trail]

wait no sqrt

right?

[indigo jetty]

no

[icy trail]

$b^2 - 4ac > 0$

[ocean seal]

querty

[indigo jetty]

no sqrt if that's what i mean

[dawn wraith]

Notice that it should be less than 0

Or am I being dumb

[marsh valley]

$b^2 - 9 > 0$

[ocean seal]

BAAPA|INDIAN ELITES

[icy trail]

if it was less than 0 you'd be rooting a negative

[indigo jetty]

yes less than 0

[marsh valley]

is this correct

[indigo jetty]

because no real roots

[icy trail]

so there would be no real roots

[dawn wraith]

No real roots.

[icy trail]

no real roots