help-27

[devout snow]

@hasty hedge Has your question been resolved?

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[main atlas]

.@rotund apex

[main atlas]

Here

[pseudo basin]

jsyk the channel's now gone and opened in your name

[main atlas]

Yeeh yeah I know

[main atlas]

He didnt knew how to open a new one

[cold haven]

If you’re redirecting someone to a channel, place a period before your message.

.@user

[main atlas]

Ill need translation

[rotund apex]

one min

[main atlas]

Ok thanks

The crying emoji was not necessary though

[cold haven]

-# I thought you were pinging him because you liked the username or something my bad.

[main atlas]

Ok no worries

[main atlas]

I did it because

[rotund apex]

2011 march not in question

[main atlas]

Ok so do you know the binomial theorem?

[rotund apex]

yes

[rotund apex]

i take it in highschool

[main atlas]

Ok, so then you know the expansion of (x+y)^n

Using combinatory numbers

Then you focus on the second, third and fourth term

Ill put the expression just so we are on the same page

[rotund apex]

I completed all the steps, but I couldn't finish the last part.

[main atlas]

Ok so its just a equation

With 3 unknowns

[rotund apex]

yes

[main atlas]

Then , isolate one unknown, for example X

And take that into another equation

And isolate one unknown again, and get the value of one unknowm

I need to go

If you have more questions, maybe someone else can help you

[rotund apex]

dude i know that already but i could not do it

[main atlas]

Send a photo of the resulting system of equations

[devout snow]

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[main atlas]

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[simple hatch]

ok i'm back and i still don't understand

[simple hatch]

why would i not just cube the whole thing in one go? why do i have to rearrange to x= Ax^1/3 and then cube it?

[supple knot]

what do you get when you cube the left side

[simple hatch]

either x^3 - A^3x or something really complicated, i'm very rusty

i mean i assume it's the latter but in that case y's that an issue

it'd look gross but it'd still work out surely

[supple knot]

definitely not x^3 - A^3 x

[polar wharf]

When you have something like (a + b),

(a + b)^2 =/= a^2 + b^2

You have to actually think of it in its true form

(a + b)*(a + b)

This is actually a case of distributive property

It would become

(a + b) × a + (a + b) × b

= a^2 + ab + ab + b^2

So you can see that squaring a sum of two objects creates a lot of terms

[simple hatch]

so rearranging is done just to keep things simpler?

[polar wharf]

Cubing them would make an even more cumbersome mess

[simple hatch]

more like cubersome, hahahaha

sorry i had to

[polar wharf]

Yes if you can separate it as you are able to in your example so that it's just one thing being cubed on each side

That is much cleaner and simpler to deal with

Rather than ending up with numerous terms

[simple hatch]

ok, 1 more thing

why do this too? i know 0.02^3 isn't gonna be the same as 41^3 but i don't get like... how this makes sense

[polar wharf]

I'm not sure where the decimal coefficient is coming from

If you just mean

[simple hatch]

sorry A = -0.02 but it's easier to just say A

at least up until this point

[polar wharf]

Oh ok

So

.02^3 is a small number between 0 and 1 right?

[simple hatch]

indeedee

[polar wharf]

When you divide something by a small number whose absolute value is less than 1

This makes the answer bigger

Try doing

1÷(.02^3) in your calculator

[simple hatch]

no no that's not ym issue, it's the same issue as before

why not cube both sides at this point?

[polar wharf]

Ohh

[simple hatch]

why is there rearranging again to move -0.02?

[polar wharf]

Well you could

There are always many roads to the same place in math

In this case it's just a small difference in the path to cube now or later

[simple hatch]

ok yeah that just clicked in my brain actually lol

[polar wharf]

The solution's method is not the only absolute way

[simple hatch]

i get it now :3 thanks man

[polar wharf]

Yw

[simple hatch]

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[paper mango]

I don't know what the asymptote is, or how to get it. Can somebody please explain?

[misty crest]

what line does the function approach as x -> inf

[paper mango]

0?

[misty crest]

y = 0

[paper mango]

I get it

[trim pewter]

the asymptote is what the function seems to approach but never does

ok maybe not the best definition for vertical ones

[paper mango]

so the asymptote would be 0 because the exponential function floats over the x axis, never reaching a y value of 0

[trim pewter]

right

[misty crest]

i mean

this is very imprecise

,w plot 2^(-x) + 1

[woven radish]

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[misty crest]

using your same logic this also has an asymptote of y = 0

[paper mango]

ok so what flatus said is considered uncorrect?

[misty crest]

yes, it is incorrect

in that it's not a proper definition at all

have you been introduced to limits yet?

[paper mango]

im looking at my notes now, and my teacher said it was "the line the exponential function continually approches but never reaches"

[misty crest]

😭

[paper mango]

no, not yet

[misty crest]

ok well formally the reason y = 0 is the asymptote here is because the limit as x -> inf of 2^-x = 0

you don't know limits formally but it just means that 2^-x gets arbitrarily close to y = 0 as we move to the right on the x axis. in other words, we can get as close as we want to y = 0 by moving far enough out right on the x axis

[misty crest]

here 2^-x + 1 doesn't get "close" to y = 0 since for example we can never be within a distance of 1/2 from y = 0 since 2^-x + 1 is > 1

[paper mango]

ah

[misty crest]

y = 1 would be the asymptote in this case

[paper mango]

OH

It's whatever is the y-intercept is...

[misty crest]

🤔

wdym

the y intercept for 2^-x is 1?

[paper mango]

wait nevermind im sort of dumb

[misty crest]

happens

[paper mango]

continue what you were saying

[misty crest]

does this not make sense?

[paper mango]

so at some point we would reach y = 0?

[misty crest]

like lets say i asked you to find a value of x so that for all values of x to the right of it, 2^-x is within a distance of say, 0.25 from y = 0

could you do that?

[misty crest]

no

there is no value of x such that 2^-x = 0

2^-x is 1/2^x

a fraction is 0 when the numerator is zero but here it is always 1, regardless of x

you can think of 1/2^x as just dividing 1 by 2 repeatedly (this makes sense for integer values of x)

like 2^-1 is 1/2

then 2^-2 is 1/4

etc

each time we divide by 2

[paper mango]

[misty crest]

we never hit 0 though of course

[paper mango]

got it

I think I understand

thanks for the help

.close

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[devout snow]

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[marble hearth]

Where am I going wrong here?

[marble hearth]

The answer key says 6500, 3000

Which doesn't really make sense

https://ess.unm.edu/resources/esspresentations_and_files/college-algebra-word-problems.pdf

Its on the final page here

[supple knot]

Yea 6500 is not six times 3000

[devout snow]

@marble hearth Has your question been resolved?

[marble hearth]

I guess its just a mistake then

[devout snow]

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[opal saffron]

Hello

[opal saffron]

Can anyone help me with my math hw

[crystal violet]

send the problem

[devout snow]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

[crystal violet]

oh ok

do u know how to solve for a variable using 1 equation

like solve for x in -5x-2y=-7

[opal saffron]

what😭

Not really

[crystal violet]

oh ok

[short hare]

they mean to seperate the variables (get x in terms of y or vice versa)

[opal saffron]

So like isolating X or 5x right

[crystal violet]

-5x - 2y = -7
-5x = 2y + 7
x = -2y/5 - 7/5

then put it into the other equation

[short hare]

see what cheescake is saying!

[opal saffron]

Thx for explaining

[crystal violet]

yw

[opal saffron]

So like do I multiply 7 times 2/5

[crystal violet]

so u plug x into the other equation 7x + 3y = 11

so it would be 7 * (-2y/5 - 7/5) + 3y = 11

[opal saffron]

That's what I did

[crystal violet]

yeah

[opal saffron]

But now I need to multiply 7 times -2/5 & - 7/5

right

[crystal violet]

correction

-2y/5

but yeah

so what did u get for the answe

r

[opal saffron]

-14y/5- 14/5 - 3y = 11

Is that correct?

[crystal violet]

so far yeah

then just solve for y

and put it into the other equation

to find x

[opal saffron]

Don't I have to add -14y/5 & 3y?

[short hare]

you do.

what cheescake meant is to find y through what you're working with right now

[opal saffron]

Yeaa ikk but I forgot how to add fractions into whole numbers

[short hare]

oh boy

[opal saffron]

It's pretty late where I live so my brain is not cooperating

[short hare]

turn 3 into (something)/5 so you can add it to -14/5 y

[opal saffron]

So I would jst need to add -14 & 3?

[short hare]

no.

[opal saffron]

oh

[short hare]

thats not how you add fractions

[opal saffron]

Then how do I add fractions

I haven't added fractions in a while tbh

[short hare]

for fractions to be added, the denominators have to be the same (one of hte methods)

for example

2 + 1/2

you cant just

add 2 to 1

so you have to change the denominator of one so it can match the other

aka the 2 here

turning it into

4/2

4/2 + 1/2

now the denominators are the same

you can add the numerators

[opal saffron]

Ok

[short hare]

(4+1)/2

=5/2

which is exactly what 2 + 1/2 is

now, you have 3y and -14/5y

you cant add the numerators directly because the denominators arent the same

3y has a denominator of 1 and -14/5 has a denominator of 5

[opal saffron]

I don't rlly think I'm supposed to get fractions in this problem tho

[short hare]

are you allowed to use a calculator for these calculations?

[opal saffron]

Yea ofc

[short hare]

...

then do so...

[opal saffron]

That's what I'm doing..

[opal saffron]

But what could I do for 3y to have the same denominator as -14/5y

[short hare]

if you're using a calculator, adding the coef's, aka 3 and -14/5 directly will do just fine

but yeah

you could turn 3y into 15/5 y

[opal saffron]

And then I add 15/5y into -14/5 right..

[short hare]

now that the two denominators are the same

you can add the numerators indeed

while leaving the matched denominators alone

15/5 y + (-14/5) y

(15+ -14)/5 y

[opal saffron]

So the answer would be 1/5y right?

[short hare]

yeah

[opal saffron]

So now I have to add 14/5 into 11 right

[short hare]

yes.

adding 14/5 to both sides will do.

[opal saffron]

.

[short hare]

yes i was answering that

wrong reply.

[opal saffron]

oh ok

Ok so before I somehow keep going I need to make sure the answer is most likely gonna end up being fractions like X is a fraction & y as well

[short hare]

ah no

i mean, the answers dont have remainders

its two whole numbers.

...assuming negative numbers are whole

but yeah, no stuff like 2.5 , 3.69 , 2.67

they're "normal" numbers

[crystal violet]

depending on your teacher probably

[short hare]

hm?

are they not talking about the solutions for x and y?

[crystal violet]

no i mean

some teachers choose nice round answers like whole numbers

it depends

on the other hand some teacher i had made answers like -491/2527 or smth like that

[short hare]

oh yeah

but dont worry, x and y both nice solutions

[devout snow]

@opal saffron Has your question been resolved?

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[austere forge]

Hello, I've a problem with TeX Live and TeXMaker, someone can help me (french if it's possible)

I have TeXMaker and I installed MiKTeX, but there was a problem with the Babel library, so I installed TeX Live, but the same problem persists (it does the same with TeXStudio), perhaps because I'm on Windows.

J'ai TeXMaker et j'ai installé MiKTeX sauf qu'il y avait un problème avec la biblothèque babel donc j'ai installé TeX Live mais le même problème persiste (cela fait pareil avec TeXStudio), peut-être car je suis sur windows

[devout snow]

@austere forge Has your question been resolved?

[void fox]

What error are you getting?

Also next time you can use the dedicated channel #latex-help for LaTeX questions

[devout snow]

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[austere saffron]

Im looking for a function that hits the points (2,4), (3,27), and (4,1024) that is never greater than x^(x!)

[polar chasm]

sounds impossible

,calc 4^(4!)

[woven radish]

Result:

2.8147497671066e+14

[polar chasm]

oh wait im stupid, i got it the other way around

[polar chasm]

Are there any other properties you want your function to have?

[tribal patio]

4^(4!) is stupidly large, and x^(x!) grow so damn fast

[austere saffron]

Yes I know

[polar chasm]

Cause otherwise we could just define f(2) = 4, f(3) = 27 and f(4) = 1024 and let the rest be constant

[tribal patio]

just use polynomials ig

[austere saffron]

But this is a case where it is useful: the number of outcome classes in a p player game set

[polar chasm]

sounds kinda like xy problem

[austere saffron]

Preferably continuous in the positives

That’s kind of it

I can’t find one

[drifting sierra]

,w polynomial through (2,4), (3,27), and (4,1024)

[polar chasm]

Would polynomial work for you?

[woven radish]

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[drifting sierra]

I guess that's above x^(x!) for x < 2

[polar chasm]

n^fib(n+1) seems to work

but its not defined on reals, unless u use binets

[polar chasm]

Your points are
2 -> 2^2
3 -> 3^3
4 -> 4^5

[austere saffron]

I suppose it would work

[polar chasm]

polynomial is here

[austere saffron]

At least for a start to get an approximate roof

[austere saffron]

This is sometimes grater than x^(x!)

[drifting sierra]

If that's all you want, you can just define it piecewise

[austere saffron]

Well, i can’t really do that? It’s hard to explain

But it’s an exact formula that I’m trying to find

I have only found those points so far

[polar chasm]

and do you think that fitting a random function will work?

Of course not (there are infinitely many such functions, there are even infinitely many such polynomials)

just send the original problem

[devout snow]

@austere saffron Has your question been resolved?

[austere saffron]

I’m just gonna ask this when I’m not busy, that ok?

[austere saffron]

I found it

.close

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[quartz bloom]

I couldn't understand, how does it follows from density theorem .

That every rational number is the interval [0,1] is the limit of some subsequence.

[quartz bloom]

I m thinking, its because , for every ε>0, there exist infinity many rational numbers between ε and any term xn of the sequence

[drifting sierra]

Are you asking specifically about that "density theorem", or are you asking for some intuition?

[quartz bloom]

I m asking , how does it follows from density theorem , reason

[drifting sierra]

Post the density theorem

[drifting sierra]

not sure how to put this formally, but there exist infinitely many rationals between any two real numbers

[quartz bloom]

..?

[drifting sierra]

If you take two real numbers x and x+epsilon, then there are infinitely many terms of (r_n) in (x, x+epsilon)

Thus there exists a subsequence of (r_n) with x as a limit

[quartz bloom]

How limit came to be x .

There no reason in my opinion

[wicked turtle]

if you want to make an explicit argument, you can start by letting epsilon = 1, then there's some n_1 such that r_n_1 is withint distance 1 of your x

[drifting sierra]

Because epsilon is arbitrary

[wicked turtle]

then let epsilon = 1/2, choose an n_2 such that r_n_2 is within distance 1/2 of your x

but you have to also enforce n_2 > n_1 because you want a subsequence

that's where you can exploit the fact that there are infinitely many rationals to choose from within that distance

[quartz bloom]

Understood.
Thank u both

.close

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[inland carbon]

find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that for all random variable $X$ following a discrete poisson distribution (in $\mathbb{N}$), $f(X)$ also follows a poisson distribution

[woven radish]

bloubbloub

[inland carbon]

I know that the answer is only id but not sure how to prove

[devout snow]

@inland carbon Has your question been resolved?

[devout snow]

@inland carbon Has your question been resolved?

[devout snow]

@inland carbon Has your question been resolved?

[devout snow]

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[grand dove]

.close

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[foggy iron]

for part b, when i subbed in x = 1/2 into my expansion, i got 25/48 and im not sure how to find an approximate value for pi for this

[lunar harbor]

What is $\arcsin \left(\frac{1}{2}\right)$?

[woven radish]

Civil Service Pigeon

[lunar harbor]

Because you can say that
$$f(1/2)=\arcsin(1/2) \approx \frac{25}{48}$$

[foggy iron]

pi/6

[woven radish]

Civil Service Pigeon

[lunar harbor]

$\implies \frac{\pi}{6} \approx \frac{25}{48}$

[woven radish]

Civil Service Pigeon

[lunar harbor]

can you finish?

[foggy iron]

ah so to get pi, u would just multiply 25/48 by 6

[lunar harbor]

mhm

[foggy iron]

ohhh okok thanks sm

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[lunar harbor]

[devout snow]

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[dreamy scroll]

can anyone help me with this one, i know about properties of determinants, but i dont know what is this supposed to mean

[dreamy scroll]

like -I + I I

then - I I + I I I

like i know the rule and all, but i have no clue what that way of doing

[hushed oyster]

Those are your elementary row operations

I + I I means multiply row 1 by -1 and add it to row 2. the same logic applies to - I I + I I I

[dreamy scroll]

this i understand

[dreamy scroll]

ok ok give me a minute to try and understand like

ohhh

so row 2 would be multiplied by -2 and added to row 3?

[hushed oyster]

You typically do ERO in order to obtain either a row reduced form or row reduced echelon form

No

row 2 would be multiplied by -1 and then added to row 3

[dreamy scroll]

okay but i ask because i dont see the logic of writing it that way, what if i need to multiply by 2? (2 as an example)

aaa never mind

i understand

thank you ajay

.close

[devout snow]

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[devout snow]

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[warm haven]

I need to do calculations faster

[warm haven]

can someone explain what this means?

and whether its viable

[pearl relic]

@warm haven please read this and tell me if you have any questions left

or at least

try to read it

ik wikipedia math sucks

https://thirdspacelearning.com/blog/what-is-short-division/ oh theres a shorter article

but BASICALLY short division is a different way of writing division (same process, written differently)

[warm haven]

oh I already use this

thanks

.close

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[devout snow]

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[sinful badge]

I need help with some Transformations

[sinful badge]

First off would we say these are good

[wicked turtle]

!original

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[sinful badge]

This was what she gave us to graph or put them on

I rewrote parts of the question

[supple knot]

,rotate

[pseudo basin]

original and transformed graphs are kinda hard to distinguish here

in your work that is

[sinful badge]

Does the flash help?

[pseudo basin]

yes now i can tell pen vs pencil

[sinful badge]

Alrighty sorry about that

[pseudo basin]

this part of the first graph is off

i have drawn in red how it should be

[sinful badge]

Alright I wasn't sure what way to bend

[pseudo basin]

the x intercept of the original is about 1.5

reflected it will become -1.5

[pseudo basin]

you should be mirror-imaging it

[sinful badge]

For which point

[sinful badge]

Alright thank you

[alpine scaffold]

hello do you still need help
?

[sinful badge]

Yes

With 8

To see if its right because I have 2 other questions I haven't completed Yet out of confusion

[sinful badge]

Ohhh I see are you talking about this

[pseudo basin]

wdym which point

[pseudo basin]

yes this one looks better now

[sinful badge]

Where I circled is where u were referring about the -1.5

Right

[pseudo basin]

the stretching one seems ok, though you did really put one phat dot at the point (0,1)

[pseudo basin]

yes

[sinful badge]

I did that because there is also a pen dot there and I just wanted to emphasis it

[sinful badge]

Alright thank you

[pseudo basin]

idt that's a good idea generally

also if anything i would prefer to see colors

[sinful badge]

Yeah I can change that after im done with the last 2

I just wanna make sure they r right

But I am stuck on the last two

So

Do I just multiply the 1/3

To the y's

I'm just not sure how this will turn out graphing with a bunch of weird fractions so I wanted to check

[pseudo basin]

as far as fractions go, thirds are not that bad. tho you may have shot yourself in the foot with your choice of scale

but yes you just divide all the y coords by 3

[sinful badge]

Haha yeah that was my teacher

Okay let me do it rw

Rq

[pseudo basin]

oh your teacher drew that?

[sinful badge]

Printed it

But she did originally

[pseudo basin]

ok

hm well aight gotta work w that then

[sinful badge]

Do my numbers look right before I actually graph

[pseudo basin]

yes

[sinful badge]

Left was original, right is new

Okay so let me graph

[dusky turtle]

Seems right

[sinful badge]

This will be hell☠️

Probably as good as it will get

[uncut crow]

that's all school is

[sinful badge]

Lmaooo

Hopefully that's right?

Then I just need help with one more

[pseudo basin]

2/3 is bigger than one grid square

[sinful badge]

Oh right

Not each line was 1

Let me fix that

Are my 1/3 okay tho

Or should they be in the middle of that box

This look better

And if so

My next and last question is about this one

I'm confused firstly on when trying to write my order pairs what the lines all are

Because from 20 to 30 , each line being 2 makes sense

But for 0 to 20 it doesn't so like im lost

I'm lost

Someone💔

I'm really tired and need to go to bed but I need to finish this

[devout snow]

@sinful badge Has your question been resolved?

[sinful badge]

😭

[devout snow]

@sinful badge Has your question been resolved?

[sinful badge]

No

[hushed oyster]

The question says "The zoo charges $1.50 extra per ticket."

This is essentially asking you to do a vertical translation

[sinful badge]

Why

[sinful badge]

Howcome it's that

[hushed oyster]

Price is what's on your y-axis right?

If price is increase by 1.5, isn't that the same thing as shifting your function up by 1.5 unit?

In the y-axis

[sinful badge]

I see

So do I write my ordered pairs?

I'm not sure what they could be with the way the scale is because the 0 to 20 is way bigger of a gap then then rest and I thought each line was 2

[hushed oyster]

your x-values remain the same, your y values increase by 1.5

[hushed oyster]

that's correct.

[sinful badge]

Yeah I understand that part

[sinful badge]

I just can't figure out my original order pair for these 3 because they are weird with the scale

[hushed oyster]

Each square corresponds to 4 years

[sinful badge]

Just for the 0 to 20 right

[hushed oyster]

Wait, why did you set it up like that?

[sinful badge]

I didn't know you could change it like that from 4 to 2 for the rest with the way this one was set up, it just seemed weird

[hushed oyster]

In the question in goes 0,10,20 etc

[sinful badge]

My teacher did that

Not me

[hushed oyster]

I think you should follow the convention of the question

[sinful badge]

What do you mean

[sinful badge]

So maybe the misunderstanding isn't just my fault then

[hushed oyster]

At the end of the day it doesn't matter which scale you use. You wll still get the same answer.

[sinful badge]

Alright thank you

Ill do it then can u check

I'm not sure how I'm meant to graph this tho

Since idk my x's due to the measurement

[hushed oyster]

Ok

[sinful badge]

Idk what to do tho

About thag

[sinful badge]

Also

How did we know it was a translation and not a reflection

Same with it not being a compression or stretch

[hushed oyster]

think about the transformations of functions. Gimme a sec, i'll write something out

[sinful badge]

Thank you

I just learned this today so

[hushed oyster]

In function notation, if the original graph is $f(x)$, your new graph is $f(x) + 1.50$.

[woven radish]

Ajay

[hushed oyster]

Every single person, regardless of their age, has to pay an extra $1.50.

[sinful badge]

The ones with the blue are mine

I couldn't figure out the x's because of the graph problem so I just did the y and matched it since you said it's a translation

[hushed oyster]

How did you get 11.25?

[sinful badge]

7.5 times 1.5

[hushed oyster]

Why multiply? You only need to add

[sinful badge]

Oh.

I multipled them all

That's fun

It's almost 4 am

I'm dying

[hushed oyster]

Hang in there

[sinful badge]

I got home from a ski trip late and finishing my work

Ill fix it tomorrow

[hushed oyster]

Ok

[sinful badge]

Id this all the time

Is*

I can't even comprehend what half of that means I'm lost lol

[hushed oyster]

Yes, those transformations are always true

[hushed oyster]

I think you should go to bed now. Getting good sleep is more important/

[sinful badge]

Can you dm me so when I go to sleep I can ask you more about this since I will eventually have a test on this and I wanna clear some things up

[sinful badge]

Thank you💗

But if you dont want that I understand

[hushed oyster]

If you ever need help just ping me. I'm usually online

[sinful badge]

Alright thank you

So much

[hushed oyster]

No worries

[sinful badge]

.close

[devout snow]

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[devout snow]

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[sand pumice]

start by listing the elements of U(12) and their inverses

[restive river]

1,5,7,11

[sand pumice]

how about the inverse of each element?

[restive river]

Hmm how do I find the inverse

[glass canopy]

is this group abelian?
if so there are two options
if not, try again

[restive river]

I don't remember that

[glass canopy]

what multiplied by 5 gets 1?

[restive river]

There is no such statements

In the question

[glass canopy]

There are exactly two abelian groups of order 4
one of them is the direct product of cyclic groups

[restive river]

5

[sand pumice]

what about the others?

[restive river]

Self inverse

All of them

[glass canopy]

And what does C2 x C2 look like?

[restive river]

Z4 and kleins 4?

[glass canopy]

yep

[restive river]

(1,1)

(a,b)

Kleins 4 is abelian?

[glass canopy]

Yes it's abelian iirc

[restive river]

I see so its abelian but not cyclic

What do I do now

[sand pumice]

think of U(n) where n<=4

[restive river]

1,3

[sand pumice]

remember here in U(12) every element is it's own inverse

[restive river]

Okay

[sand pumice]

also 12=3•4

[restive river]

Hmm

[sand pumice]

what about U(3)?

[restive river]

1

2

[sand pumice]

okay so is it reasonable to try U(3)×U(4)

[restive river]

I don't think so

I don't get it how is related

[sand pumice]

okay wait let's work with kleins 4

[restive river]

Okay

[sand pumice]

you have every element in U(12) as it's own inverse, and how many generators does it have

||sorry i thought you knew kleins 4 can be represented as {1,3,7,11}||

[restive river]

Ohh i didn't know

[restive river]

I don't see any

[sand pumice]

well any two elements can generate it

given neither of them is 1

[restive river]

All of them except 1?

[sand pumice]

you could try any product involving U(3) and U(4)

[sand pumice]

ye

[restive river]

And that will give me the isomorphism?

[sand pumice]

well you have to construct one

<@&268886789983436800>

[restive river]

I see okay lemme try when I am done I will ping you

[sand pumice]

👍

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[runic prawn]

how old are you?

[marsh trail]

Probably trolling

[pseudo basin]

<@&268886789983436800> troll

[restive river]

1.999999... + 1.999999... = 4

[pseudo basin]

!nosols also don't feed the troll

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

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[copper harbor]

pls don't feed trolls thx

[devout snow]

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[onyx badge]

hi

[alpine scaffold]

hewo

[onyx badge]

how do i write a truth table with ( p v ~q) ^ (q->r)?

[alpine scaffold]

oh.

[pseudo basin]

why did you ping me bruh

[onyx badge]

the if then statement making me confused

[alpine scaffold]

uhh out of my league. contact helpers if no one responded

[pseudo basin]

rephrase "if A then B" as "(not A) or B"

[onyx badge]

should i make a logic gate first for it

[pseudo basin]

if you wanna draw a circuit diagram for it then go ahead, but your goal is a truth table, so...

[onyx badge]

so if i rephrase it, it should be like this? (~A v B)?

[near jolt]

yes, the q->r is literally just saying "if q were to be true, then r must be true", so this means that either q is false (in which case sure, no constraint on r), or q is true, in which case the only constraint is that "r must be true"

what i said is literally (~A v (A ^B)) which is the same as (~AvB)

[onyx badge]

so if im writing the truth table it would go like this? A | B | R | ~B ?

[near jolt]

What is R

[onyx badge]

the q->r

[near jolt]

well A, B are just example that ann gave

[onyx badge]

im using this btw

[near jolt]

so the symbols are just p q r

[onyx badge]

yes

[near jolt]

so can you rewrite it with p,q,r?

using the symbols in the question

[onyx badge]

p | q | r | ~q

[near jolt]

shouldn't there be p v~q and q->r and ( p v ~q) ^ (q->r) too?

[onyx badge]

oh yes that too

sry this lesson was just introduced to us

[near jolt]

its more like a streamlined process: if we know p,q,r, what can we immediately deduce: aha, the truth of ~q. And then what can we deduce? Aha the truth of p v ~q,...

then eventually you deduce the truth of ( p v ~q) ^ (q->r)

the table is sort of making sure that each deduction is immediate from what you have

[onyx badge]

oh yes i know the pattern for i

searched a few stuff

[near jolt]

like this for example

[onyx badge]

ohh if both if false then its false

[near jolt]

wait what

P->Q is true when P is false and Q is false

[onyx badge]

on the bottom part

oh wait nvm

it was a T

mb im using dark mode

so as long as Q is false its false

[near jolt]

no, P->Q is true when Q is false and P is false

"if 1 isn't a number then 2 isn't a number" is a true statement

[onyx badge]

ohh

[near jolt]

because the "if 1 isn't a number" is false

like i can say "(insert absurd false statement) -> (insert another absurd false statement)" and it would be a true statement

[onyx badge]

how many rows will it be for the truth table 8?

[near jolt]

wdym truth table 8?

[onyx badge]

the rows

[onyx badge]

like this one it has 4

[near jolt]

well since your initial conditions are only about whether p,q,r is true, there should be 8 rows

[onyx badge]

okiee ill go create one

[near jolt]

since there are 2 possibilities for p,q,r, which totals to 2^3=8

the rest of the columns are basically "what can we deduce given wherther p,q,r are true/fals"

the inbetween statements like q->r are just friends we made along the way

[onyx badge]

is this right

or im missing something

[onyx badge]

just find the pattern right

oh wait i forgot the ~qq

[near jolt]

you forgot the actual question: ( p v ~q) ^ (q->r)

[onyx badge]

oh yea that too

oke now its ready

[near jolt]

if you want a tip you can just look at the columns you made and ask yourself can i deduce p v~q immediately knowing the previous truth value? if the answer is no, then you might have missed a column inbetween

[onyx badge]

okie thanks for the tip

might miss one when its exam day

[near jolt]

but honestly if you simply have p|q|r|( p v ~q) ^ (q->r) it wouldn't be "wrong". You are just skipping a lot of steps

[onyx badge]

is this right

[near jolt]

great!

[onyx badge]

how do i do the or part

so T and F is still T?

[near jolt]

if you are stuck, if p is T, then try replacing p with an actual true statement.

Like ill give you an example where p,q,r T. Let's replace p,q,r with "1 is a number", "2 is a number" and "3 is a number"

Then p or ~q is saying "1 is a number OR 2 is not a number" and since 1 is indeed a number, p or ~q is true

[near jolt]

precisely!

OR only requires one of the two statements to be true

[onyx badge]

so if both are false its false?

[near jolt]

yes

it's essentially interpreting OR as used in your day to day language

[onyx badge]

right?

[near jolt]

you can't say "p or q" is true when both p and q are false, you'd just be lying lol

[onyx badge]

woo im learning

[near jolt]

fire

good

looks all correct

[onyx badge]

okie yippiee

[near jolt]

and if this feels unintuitive to you you can just remember the tables for each operation (which might be real pain to remember)

[onyx badge]

?

[onyx badge]

i have a bi of a short term memory

[near jolt]

also this might not apply to real world scenario in certain cases because the statement itself is uncertain. something like "i will win 100 million dollars" does not have a intrinsic truth value atm because we genuienly dunno if the statement is true or not. This is only application when p,q,r have genuien truth value

[onyx badge]

what compound proposition would that be?

conigency?

[near jolt]

yeah replace p,q,r with universal statements that are True/False so you have some intuition

[near jolt]

can you clip the whole table, i don't wanna go back and forth between 2 images

[near jolt]

what does compound proposition mean

[near jolt]

the third row: the statement "1 isn't a number implies 2 is a number" is technically true, because 1 is a number, the whole statement sort of falls apart to being true if your assumption is false to begin with.

[onyx badge]

i think like combining propositions using logic

[onyx badge]

so i did the opposite?

[near jolt]

if you are asking about "i will win 100 million dollar", my point is it isn't a proposition to begin with.

[near jolt]

yeah "q->r" is essentially the constraint "if q were true, then r must be true": notice how it doesn't have any constrain when q is false.

[onyx badge]

so instead of T in the first row its F?

[near jolt]

can you explain why?

if q is true and r is true, you are saying that "q -> r" is false?

is the statement "if 1 is a number then 2 is a number" true?

[onyx badge]

oh wait no

its both true

[near jolt]

ok try doing it with q true and r false

try replacing it with actual true and actual false statement

conbine them, and think whether it'd "q->r" sound true/not

[onyx badge]

so if number 1 is false and 2 is true then its false?

[near jolt]

what is number 1?

[onyx badge]

like if 1 is a number and 2 is not a number then its false

[near jolt]

while your conclusion is true can you sorta explain why?

what does q->r say in this case?

[onyx badge]

even though the first number is false the 2nd statement is still true?

[near jolt]

hmm i kinda dont understand what you mean: "first number is false" doesnt makes sense to me...

remember q is the statement "1 is a number" and r is the statement "2 is not a number"

wait maybe i mightve not explained something clearly. by "1 is a number" i literally mean "the symbol 1 represents a number" which is a obviously true statement

maybe "1 is a positive integer" makes more sense

[onyx badge]

to be honest i still dont get it i might just be dumb

[near jolt]

let me ask you a question: is the statement "if 1 is a positive integer then 2 is a positive integer" true?

[onyx badge]

yes true

oh

[near jolt]

now let us define q to be the statement "1 is a positive integer"
and r to be the statement "2 is a positive integer".

Is q true? Is r true? and is q->r true?

[onyx badge]

yes its true

[near jolt]

notice that q->r literally just means "if 1 is a positive integer then 2 is a positive integer"

[onyx badge]

yes

so if 1 is a negative integer then 2 is a negative integer

[near jolt]

well is this statement true?

[onyx badge]

yes true

so when its 1 is a negative integer then 2 is a positivie integer then its false?

[near jolt]

it is still true: if your assumption (the if part) is false, then you can go crazy on the conclusion, and it will always be true

[onyx badge]

oh its still true

[near jolt]

i can say "if it rains right now i will bring an umbrella"
It would be true if it doesn't rain and i still brought an umbrella

[onyx badge]

so it would be like this?

[near jolt]

excellent

[onyx badge]

yayy

[near jolt]

yeah you might be more familiar with the example "if it rains right now i will bring an umbrella"

if this I lied, its false, otherwise it is true

so in the case where it doesn't rain, i technically did not lie, so "if it rains right now i will bring an umbrella" is always percieved as true

does that make more sense?

[onyx badge]

yes i understand it better

[near jolt]

so in full generality: "q->r" is always true if q is false.

because technically I ain't lying since q is not true anyways

[onyx badge]

that took me a while

[near jolt]

ig "p is true" can be interpreted as "i wouldn't be lying if i said p"

so "if 1 is negative then 2 is positive" is true because I ain't lying: 1 being negative is just not the way things are

[onyx badge]

as long as youre not lying itts true

[near jolt]

yeah you can intuitively interpret it as such

this whole logic this is to formalize such intuition to apply to general cases

instead of actual statement thats either t/f like "it is raining right now here" and "1 is a positive number" its a generic "p"

[onyx badge]

so the next part is now the both parts

[near jolt]

this should be easy for you

[onyx badge]

for the and gate aslong as theres a false its false right

[near jolt]

yes

like id be lying if i said "1 is a positive int and 2 is not a positive int"
I would also be lying if i said "1 is not a positive int and 2 is a positive int"

int is slang for integer for anyone who just joined the chat

[onyx badge]

alright lemme put all of it

though what does tautology contradiction and contingency mean

since i need to identify the compound proposition

[near jolt]

tautology is like saying "if is rains right now, I am bringing umbrella" but it is not raining.

technically i'm not lying but the statement is kinda pointless.

[onyx badge]

so this is not tautology

[near jolt]

contradictions are statements that cannot be true altogether. For example, the three statements: "it is raining" and "if it is raining then i am bringing an umbrella" and "I am not bringing an umbrella". The three statement together is a contradiction: If I said all three statements I would contradict myself.

[near jolt]

what does "this" refer to

[onyx badge]

well on the table its true and false and in ttautology it needs to be all true right

[near jolt]

Well shoot i explained it wrong....

there is a formal notion of tautology in logic mb

Tautology is where the statement is always true.

[onyx badge]

woo yes i understood it

[near jolt]

contingency is when it can be true or false

[onyx badge]

oh then this is conigency

[near jolt]

and contradiction is statement that is always false

i don't have your table in the end

so idk lol

[onyx badge]

oh wait

[near jolt]

yes the ending statement is a contingency

because it can be true or false

[onyx badge]

owkieee

[near jolt]

like p and ~p is a contradiction, cuz there is no universe that is true

its like saying "it is raining and it is not raining"

i oughta be high if i say that

[onyx badge]

would this topic be linked to quantum physics or nah

[near jolt]

i think basic logic is foundational in working with arguments.

statements "if A then B" are essentially these logic gates: "A->B"

[onyx badge]

so just in programming

[near jolt]

and sometimes people use these to formulate math statement

[near jolt]

it is used in math too

you can state some statements using purely symbols

although you can always state it using word

although idk if it is used quantum physic

[onyx badge]

using symbols would make me more confused lol

[near jolt]

but u will see statements like "if A, then B" and it is crucial for you to understand the ideology that if im not lying im right.

when A and B are statement that are either true/false.

[onyx badge]

so it just applies to everything

[near jolt]

its sort of building your intuition of logical reasoning, beyond that, prob no application in quantum physics

but its good that u seem to have a decent grasp on q->r

and other gates

[onyx badge]

yes now for the other gates

[near jolt]

great

[onyx badge]

this one i kind of understood but not the nor gate

so my understanding is (a n b) v (~a v b)?

[near jolt]

i have no idea what these gate symbol mean i don't do CS lol.

[onyx badge]

oh wait

this

so the part im having some trouble with is the smooth triagle with a sphere on top

[near jolt]

if A=0 the Y=1 and if A=1 then Y=0?

[onyx badge]

like idk how to write that in compound proposition

[near jolt]

it's literally "~A"

[onyx badge]

oh

[near jolt]

it makes sense, replace 0 with false and 1 with true

if A is false, then the output is true

if A is true, then the output is flase

this is exactly what ~A does

[onyx badge]

so b will be the not?

~b?

[near jolt]

yeah the truth value when b passes through the NOT gate will be the truth value of ~b

[onyx badge]

so will it be a v ~b?

[near jolt]

for what

where did a come from

we are talking about the NOT gate right?

[onyx badge]

the nor gate

[near jolt]

oh

i thought u meant the NOT gate when you are talking about triangle with circle on top

[onyx badge]

oh i said smooth triangle

[near jolt]

it means the same as it's same. p,q goes in "neither p not q" comes out.

[onyx badge]

so both will have a NOT?

[near jolt]

so say p is "1 is a positive integer", and q is "2 is a positive integer", then nor gate returns the truth value of "neither is 1 a positive integer, nor is 2 a positive integer" (clearly false btw).

[near jolt]

can you write it down?

a,b goes in, what comes out?

[onyx badge]

(~a v ~b)?

[near jolt]

neither... nor... means both are false.

if a is "1 is a positive integer" and b is "2 is negative integer" then it returns the truth value of "neither 1 is a positive integer, nor is 2 a negative integer" (still clearly false, since 1 is a positive integer).

however, in my case, (~a v ~b) returns true since ~b is true.

[onyx badge]

how would that be constructed

so just a v b? since neither

[near jolt]

so intuitively "neither a, nor b" means "not a, and not b"

[near jolt]

a or b says one of a, b is true. but we want neither of a,b to be true for it to return true

[onyx badge]

oh so was the a v ~b right?

oh wait nvm

[near jolt]

still not quite... you can see with my comment here it means a nor b is true when both a,b are false

[onyx badge]

oh wait so both are false

would it be constructed as ~(a v b)?

[near jolt]

either this, or ~a ^ ~b

[onyx badge]

50/50 gamble

[near jolt]

they have the same truth table.

[onyx badge]

so both are correct

[near jolt]

yeah

try constructing the truth table for ~a ^ ~b, and ~(a v b)

[onyx badge]

though how would i answer it on the truth table having the not outside the parenthesis

[near jolt]

you'll see.

[onyx badge]

oh wait when did the v turn into a ^

[near jolt]

a NOR b is true when both a, b are false

[onyx badge]

the gate changes too?

[near jolt]

its saying precisely (~a and ~b)

[near jolt]

wdym

[onyx badge]

but the nor is V

[near jolt]

nor isn't on the table

there are two possible definition using the symbols we have

[onyx badge]

what would it be

[near jolt]

it's the same

you can prove they are the same

like ~~~a is the same of ~a

nothing is wrong if you say NOT gate is defined to be ~~~a

though quite redundant

[onyx badge]

oh right since both of it is not ~a and ~b

so its now ^

?

[near jolt]

yeah its not a and not b

[onyx badge]

okie

time to make the table

[near jolt]

not (a or b) is also good

whichever suits you

there's no wrong answers between the two.

[onyx badge]

alright

[near jolt]

as an exercise you can show that not (a or b) is the same as (not a and not b)

or in logic notations, it means that "not (a or b) <->(not a and not b)" is always true, regardless of the truth value of a and b

[onyx badge]

i have a question

my friend has an answer like (a v ~b)

[near jolt]

try and show your friend is wrong by constructing the truth table of (a v ~b), and show them that it is different that the truth table NOR gate gives

[onyx badge]

oke lemme construct

[near jolt]

you can intuitively interpret Nor gate as a not gate after a or gate

and Nand gate as a not gate after the and gate

i suspect thats what they mean when they call it Nand and Nor

so Nand is not(a and b) and Nor is not(a or b)

[onyx badge]

ohh so it just the opposite

he got it from chatgpt

[near jolt]

aint no way.... chatgpt oughta be smarter than that nowadays

i just asked it

[onyx badge]

wait tthe A doesnt have a ~?

[near jolt]

wdym

no

[onyx badge]

it has like a not before going in the nor gatte

[near jolt]

its ~(a v b)

[near jolt]

oh in this diagram

idk

im just giving you the definition of the Nor gate

[onyx badge]

how would it work out if its like that

[near jolt]

if you give Nor gate input a,b then it spits out ~(a or b)

[onyx badge]

what if it consumes an ~a,b

[near jolt]

same formula just plug it in

input Nor gate with input x,y then it spits out ~(x or y)

plug in x=~a and y=b

im using x,y to not get confused with your a,b

[onyx badge]

for this it would spit out ~(a or b) aswell

[near jolt]

^its this

you are getting the symbols confused

if the input is x,y, it outputs ~(x or y)

and you basically said your "x" is (~a), and your y is "b"

like in the very beginning, (p v ~q) ^ (q->r) is like (p v ~q), (q->r) passing through the AND gate

[onyx badge]

so it would still be or but (a v ~b)?

[near jolt]

idk how you got that

plug in ~a into x, and b into y

i dont see how the ~ in front of ~(x or y) should go away

its outside a bracket

[onyx badge]

so would it be like ~(~x or y)??

[near jolt]

it would be ~(~a or b)

try not to reuse symbols as in the definition.

plug in ~x into x would sound weird

[onyx badge]

oh now i understand the way u were explaining itt

[near jolt]

yeah x, y are any logical statement

~a is just an instance of a logical statment

[onyx badge]

so its ~(~a or b)

[near jolt]

good!

and the gate on the top is (a or b).

so what does the final NOR gate do?

[onyx badge]

wait final nor gatte?

u mean the one towards q?

[near jolt]

yeah i now just realized that circle means something different lol

my gate reading is bad

[onyx badge]

oh thats just a pointer to the Q

[near jolt]

the gate on the top is an AND gate so my answer here is wrong

it should be (a and b)

anyways, what would Q be?

[onyx badge]

yes

hol on it would be

(A n B) v ~(~A v B)

[near jolt]

first try, and correct!

[onyx badge]

woooo

[near jolt]

you should view p v q as a logical conjunctions just like p, q. and these gates as simply plugging in these logical conjunctions

[onyx badge]

oh btw question

i dont have to change the or to an and right

like ~(~A n B)

[near jolt]

you don't why would you?

[onyx badge]

oh nvm

i dont need to change it

[near jolt]

yeah it's just plugging in

changing v to n fundamentally changes the output.

u don't wanna do that

that'd give you a faulty gate

[onyx badge]

learning circuits while in it 🥀

time to do the table

am i doing it rihgt

@near jolt?

[near jolt]

you mistakenly did ~B on the ~A column lol

classic misread the symbols type of mistake

[onyx badge]

oh yea

it was supposed to be fftt