help-49

[near geyser]

For no confusion

Thanks

.close

[midnight plank]

Channel closed

Closed by @near geyser

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[karmic mist]

AC parallel BP

BAC=?

[shell wigeon]

PA and PB are tangent to the circle, right?

[worn crown]

math server wow

[karmic mist]

thats all i could do

[karmic mist]

yeah

[shell wigeon]

That's a good start

What can you say about the triangle ABP?

[karmic mist]

uhmmm

[steep rune]

can you please translate this to english?

[karmic mist]

okay wait a sec

A and B are tangent points [PB // [AC] m(APB) = 40° According to the given information above, what is the measure of m(BAC) = (\alpha ) in degrees? A) 40 B) 50 C) 60 D) 70 E) 80

[grand pond]

Thorfinn

[shell wigeon]

Since PA and PB are tangent to the circle, you should be able to say something about the segments PA and PB and about the triangle ABP

[karmic mist]

oooh i got it

they are same length

[shell wigeon]

Exactly

[karmic mist]

so answer is 70

tysm

im so tired that i couldn see the tangents

[PE is tangent to the circle at point T. (|PT|=|BT|), (m(\widehat{TAB})=76^{\circ }) According to the given information, what is (m(\widehat{BTA})=x) in degrees? A) 66 B) 64 C) 62 D) 60 E) 58

[grand pond]

Thorfinn

[karmic mist]

i got the answer 52

[steep rune]

what are those purple equality sign looking things?

[karmic mist]

it means these two lines are same lenght

BT and TP

[steep rune]

ok

[midnight plank]

Show your work, and if possible, explain where you are stuck.

[karmic mist]

oh okay

i cant take picture of paper cause i dont have my phone rn

so thats all i can do

[small jasper]

did you assume that these two angles were equal

,calc (180-76)/2

[grand pond]

Result:

52

[karmic mist]

uhhh

how?

[small jasper]

I'm not saying they're equal

I'm asking if that's what you did

[karmic mist]

no

[small jasper]

so how did you go from what you wrote to 52

[karmic mist]

wait a sec

okay so

ATP=2a/2

ATP=a

a+a+104=180

a=38

oh wait

sorry

i actually made it

answer is 66

[small jasper]

good

[karmic mist]

thanks for help

[small jasper]

[midnight plank]

If you are done with this channel, please mark your problem as solved by typing .close

[karmic mist]

.close

[midnight plank]

Channel closed

Closed by @karmic mist

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dawn dagger]

Is the following proof okay or is it not rigorous?

[placid spoke]

looks rigorous to me, though i'm not sure what you mean by "since pk | m as well, it is..."

the "it is" doesn't make sense imo

i'd just delete that and you're good

[dawn dagger]

ok ty

.solved

[midnight plank]

Channel closed

Closed by @dawn dagger

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[agile root]

I am studying a bit of classical logic and I want to know if this proposition is true

P: 3+4 = 9 -> the universe is smaller than the milkyway

[steel crest]

it's true because mathematicians consider all implications with false premise to be true

it's kind of like saying "If (false thing), then I'll eat my hat"

or "If (false thing), then I'm a monkey's uncle"

[agile root]

is there a way to formalize these?

[steel crest]

yeah ,

$\perp \vdash$

[grand pond]

gfauxpas

[steel crest]

wait, looking for the right latex for it

yeah that's right

this looks very strange, but i'll go over it

$\perp$ is the symbol meaning a statement defined to be false

[grand pond]

gfauxpas

[steel crest]

$\vdash$ means "therefore"

[grand pond]

gfauxpas

[steel crest]

so this means "false, therefore" and me not writing anything to the right of "therefore" means anything can go there

so you can also write

$\perp \vdash p$
where $p$ is any statement

[grand pond]

gfauxpas

[agile root]

is this axiomatic or do we have a proof of this?

[steel crest]

it's part of the definition of implication

so, axiom / definition

[agile root]

ohh

[steel crest]

it's both , really

because when you want to use the implication concept, you're assuming you know what it means when the hypothesis is false

so it's an axiom, but you're assuming it as part of the definition of implication, it's both a defn and an axiom in that sense.

[agile root]

are axioms and definitions not synonomous?

[steel crest]

in general no. a definition says what something means, an axiom says something is true

[agile root]

as i was learning linear algebra yesterday, my tutor talked about the vector space axioms. Would it not be equally valid to say a vector space is defined to be a set with these operations?

[steel crest]

yes, that's an example where it's both

a vector space has a definition: it's a space that obeys these axioms

[agile root]

ohh that makes sense

tysm, i understand what i asked!

.close

[steel crest]

np

[midnight plank]

Channel closed

Closed by @agile root

Use .reopen if this was a mistake.

[steel crest]

wait

.reopen

[midnight plank]

✅ Original question: #help-49 message

[steel crest]

@agile root I recommend reading the first chapter or two of "Introduction to Logic and the Methodology of Deductive Sciences" by Alfred Tarski. his notation is dated but it goes over the nature of definitions and axioms and implications with false premises

youc an find the pdf online

[agile root]

alright, i will check that out ❤️

4th edition?

[steel crest]

I dunno, doubt the edition matters

[agile root]

okay!

ty

.close

[midnight plank]

Channel closed

Closed by @agile root

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[remote spindle]

hi, im struggling to prove this by natural deduction

[remote spindle]

or more precisely im unable to prove it in the way ive been taught natural deduction

this is my work so far but the proof from 3,2,2 is missing

i think i need to use the premise R -> ¬P somehow but i just cant figure out how

[midnight plank]

@remote spindle Has your question been resolved?

[remote spindle]

nvm i found another way

.close

[midnight plank]

Channel closed

Closed by @remote spindle

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[median fossil]

can someone explain to me what the hell i'm missing here?

[median fossil]

C makes no sense for me

.close

[midnight plank]

Channel closed

Closed by @median fossil

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[coral belfry]

,tex
Hello there. Suppose we have a sequence $ c_n $ and the following is true:
\
$$ c_n \leq \frac{1}{2+\frac{1}{2n}} $$
\
if we prove that \
$$\forall \varepsilon >0 , \exists n_0 \in\mathbb{N} \ \text{s.t.} \forall n\geq n_0 : \ \lvert \frac{1}{2+\frac{1}{2n}} -\frac{1}{2} \rvert < \varepsilon $$ \
, then can we say that $c_n $ converges to $\frac{1}{2} $ ?

[grand pond]

fijokazż

[coral belfry]

my brains rlly weird at the moment and i cant remember why thats the case

[wicked sequoia]

No

[coral belfry]

hmm what am i missing then?

[wicked sequoia]

You only have an inequality, that's not because the right term converges than left one also converges

[coral belfry]

true

[wicked sequoia]

That's like saying Un ≤ 1+1/n

You have no idea it converges

[coral belfry]

i understand, but i dont remember what i gotta say next to prove convergence to 1/2

[wicked sequoia]

Well you'd have to have a second inequality or something like that

[coral belfry]

(c_n does converge to 1/2 )

[wicked sequoia]

To use squeeze théorème for example

[wicked sequoia]

You want to prove ut ?

It*

[coral belfry]

yeah

[wicked sequoia]

Well what you have is unsufficiant

I don't know about your exercise so...

[coral belfry]

hmm what if i show that 1/2> c_n ?

i think i can

[wicked sequoia]

Well it's still not sufficiant

It's pretty much exactly the same equality

[coral belfry]

oh wait true lol

my brain isnt working mannnn

[wicked sequoia]

You'd have to have something like cn > ...

[coral belfry]

yeah i see why

[wicked sequoia]

Like cn ≥ vn with vn converging to 1/2 for instance

What is your exercise ?

[coral belfry]

lemme write it

,tex
$ c_n = \sqrt{n^2 +n} -n $

[grand pond]

fijokazż

[coral belfry]

i used conjugate then Bernoulli's inequality to get my first ineq.

[wicked sequoia]

Do you know about limited developpement ?

[coral belfry]

Bernoulli's says (1+x)^n >= 1+nx right?

[coral belfry]

i dont think so

[wicked sequoia]

You did not study asymptotic expansion?

[coral belfry]

no we are at the beginning of calc 1

[wicked sequoia]

Like Taylor series, all of that

[coral belfry]

nono

[wicked sequoia]

Okk

Well you still have this inequality

Sqrt(1+x) ≤ 1 + 1/2x

[coral belfry]

huhhhh

wait

this is Bernoulli's thing right?

[wicked sequoia]

Concavity of sqrt

[wicked sequoia]

Well I think Bernoulli is only for integer exponents

[coral belfry]

wait am i dumb lemme check again

[wicked sequoia]

Did you learn about convexity?

[coral belfry]

youre right its for integers

[coral belfry]

no

oh man i thought i was in the right path

i can definitely show that c_n <= 1/2

but idk how to find another sequence that binds c_n from below

[wicked sequoia]

Well Taylor series gives you a second terme, and you do have the inequality sqrt(1+x) ≥ 1+1/2x -1/8x²

I think if you did not study Taylor series, you still can prove the inequality with a function study

[coral belfry]

we cant use series expansions unfortunately

we actually arent even using derivatives or integrals either

so a lotta ways are invalid here

[wicked sequoia]

Well not even derivatives ?

[coral belfry]

nope lol

[wicked sequoia]

I don't have a lot to work with...

Give me a few minutes I gotta finish something

[coral belfry]

okeoke

i tried starting from
|c_n -1/2| and i arrived at a different kind of sequence which seems even harder to prove it converges to 0, but perhaps its more likely? idk man

[wicked sequoia]

Do you have equivalents ?

I suppose not

[coral belfry]

wdym?

,rccw

[coral belfry]

ignore the arithmetic mistakes i made, and the second line is what i found

i split it in two just to see if theres anything there but idk

our professor hates us i guess

[wicked sequoia]

Ok I have something

It's very bizarre to do it without any taylor series but I mean if he wants to

First multiply by the conjugate

Wait a sec

[coral belfry]

howd you get the first inequality tho?

[wicked sequoia]

Well if you do not even have this one it'll be complicated

[coral belfry]

hahah guess what

[wicked sequoia]

You have it by concavity of the logarithm function

But if you did not study it

[coral belfry]

we havent:)

[wicked sequoia]

Well I mean

[coral belfry]

concavity involves derivatives no? im not sure what it means in english

[wicked sequoia]

Ok I over complicated things

You can just stop here

[coral belfry]

wdym?

[wicked sequoia]

Well not if you have a correct professor

[coral belfry]

our prof asked us to use the epsilon definition of a limit

i initially did it like that but he said its a nono

could we maybe prove the concavity or wtv its called via induction?

[wicked sequoia]

If you don't have √(1+x) ≤ 1 + 1/2x I don't think you can do anything

To be fair, the usual way to prove it is by concavity of √, you probably can do it by a function study as it's an order 2 polynomial

You can use quadratic properties ?

Roots, minima, etc

[coral belfry]

perhaps

but we cannot differentiate/integrate anything

[wicked sequoia]

Square both sides of the inequation

1 + x ≤ 1 + x + 1/4x²

[coral belfry]

1/(4n²)>0

[wicked sequoia]

So 1/4x² ≥ 0 which is always true in R+

[coral belfry]

wait i think that could be fine

[wicked sequoia]

You have the inequation as a result

[coral belfry]

it seems to me like its the only method

[wicked sequoia]

Using the epsilon definition here is extremely ineffective

[coral belfry]

i mean now that we proved the inequality, squeeze theorem uses epsilon def so we good

we dont have to prove the squeeze thank god

maybe he misspoke by saying which definition to use so idk

anyways thank you ill do it this way

.solved

[midnight plank]

Channel closed

Closed by @coral belfry

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wispy flax]

can someone help me find the domain of functions it’s algebra 2 and i’m about to lose it right now

[wispy flax]

https://tenor.com/view/praying-crying-downfall-sad-tears-praying-gif-7785197299162436598

it’s so over

it’s due tomorrow bro

[oak kelp]

which question do you need help with?

[wispy flax]

the circled ones with green writing

i got thrown wrong

it’s test corrections for points back

but idk why it’s wrong or how to get it right 😭

[oak kelp]

I presume this is one of them?

[wispy flax]

yes i hate that one

square roots are so dumb

[oak kelp]

so, you rightly guessed that the expression in the sq. root cannot be negative.

however, you did not account for the fact that the square root is in the dneominator of a fraction.
as mentioned by the writing, the denominators of fractions can never be 0 (division by 0 is undefined).

so this becomes a strict inequality.

[wispy flax]

why does it have to be greater than 1 and can’t be equal to it? 💔

i chose D

[oak kelp]

if you let x = 1, the denominator becomes sqrt(1 - 1) = sqrt(0) = 0.

[wispy flax]

OHHHHH

[oak kelp]

can you have 0 in the denominator of a fraction?

[wispy flax]

no

okay i get it now

[oak kelp]

yes, and that's precisely why x = 1 is banned from the domain.

[wispy flax]

okay tysm

[oak kelp]

as for the odd function question, do you still need help with that?

[wispy flax]

yesss

i was just writing stuff but i don’t understand fr 😭

[oak kelp]

odd functions are where $f(-x) = -f(x)$. in other words, if you substitute -x for x everywhere and it turns out to be a negative copy of the original function, then it is odd.

[grand pond]

Hyacine

[wispy flax]

how do you figure that out ?

omg wait

nvm i don’t get it

[oak kelp]

it's a definition.

there are also even functions, where $f(-x) = f(x)$.

[grand pond]

Hyacine

[subtle blaze]

odd functions look the same if you rotate 180 deg around the origin

[wispy flax]

so do you set f(-x) equal to what you already have like i did

[subtle blaze]

even functions look the same if you reflect across the y-axis

[oak kelp]

though I will say, this question has multiple answers. your answer is technically also correct.

[oak kelp]

yes.

the function you circled is neither even nor odd.

[wispy flax]

so even is reflection and odd is a rotation?

[wispy flax]

ohh i see

[subtle blaze]

not is but you can visualise it as such

[wispy flax]

okay thanks :3

[subtle blaze]

also interestingly, you can decompose any function into an even and odd part

[wispy flax]

i tried that but i got stuck

cause when i try to subtract form the other side it was jus 2x^3

[oak kelp]

applying that to your function gives you (-x)^3 + 1 = -x^3 + 1, which is neither f(x) nor -f(x).

[subtle blaze]

if you add f even and f odd you get f back

very cool

[oak kelp]

not OP, but thank you for the insight!

[wispy flax]

how do you write it then? i was tryna copy from google but id didn’t know what f(-x) meant

[oak kelp]

say we have f(x) = x + 1. how would you find f(3)? (don't calculate - just tell me the steps you would do.)

[wispy flax]

you swap in 3 for x and solve

[oak kelp]

correct!

[wispy flax]

so it would be 3 + 1

[oak kelp]

so f(-x) is just swapping in -x for x.

for example, for f(x) = x + 1, f(-x) would be -x + 1.

[wispy flax]

okay i see

[oak kelp]

but if f(x) was itself -x + 1, f(-x) would be -(-x) + 1 = x + 1.

so basically the same thing as we do with other functions and numbers.

either way, that question seems flawed.

[wispy flax]

how come C is the right answer? i just picked something random because i wasn’t sure what to do

so

[oak kelp]

wait was your answer A or C?

[wispy flax]

would i do like x^3 + 1 = -x^3 + 1?

[wispy flax]

A

the teacher circled the right answer

[oak kelp]

A is odd.

oh in that case then yes, C is right.

I thought for some reason that the correct answer was A, sorry.

[wispy flax]

no that’s fine :3

[oak kelp]

this is the right way.

and we see from here that this is neither the original function nor the negative version.

so it's neither even nor odd (so definitely not odd), which is what the question is asking for.

[wispy flax]

ohhhh

okay i see

[wispy flax]

what about the bottom one for this one

[oak kelp]

A is definitely wrong.

x = 5 will give you a negative value under the root.

in fact, any x less than 9 will do so.

[wispy flax]

oh so do you just plug it in

into the equation i mean

[oak kelp]

not necessarily. you know that expressions inside square roots cannot go under 0. so find the value of x that makes the expression 0, and ban all values less than that (or greater than that if -x).

[wispy flax]

oh okay i get it now

tysm!

[oak kelp]

glad to help!

[wispy flax]

can you help with one more thing

how do you do this one

[oak kelp]

multiply both sides by the denominator to get it off the bottom.
then, pull any terms with y to the left, and factor y out, then send everything that isn't y back to the right side.

[wispy flax]

was i supposed to swap the x and y

[oak kelp]

normally I would swap x and y around from what you wrote, because y = f(x).

I'm not sure if your teacher allows you to write it like this though. if they do, this isn't wrong either.

[wispy flax]

okay thank you !

[oak kelp]

glad to have helped! anything else?

[midnight plank]

@wispy flax Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[last stone]

Can i remove the fraction by multiplying every subject with 2?

[lapis vector]

yes

[last stone]

So 10 -2x -2x^2 + 10?

[lapis vector]

well you can't just get rid of the fraction entirely

by multiplying by 2, you only get rid of the denominator, not the whole subject

so you'd get 10+5x-2x-2x^2+10=0

does this make sense?

[last stone]

So

-2x^2 + 8x + 20 = 0

@lapis vector

[lapis vector]

whats 5x-2x

?

[last stone]

Oh so it’s not 10x?

[lapis vector]

what

back up

[last stone]

Kk then

[lapis vector]

so first you multiply by two, what do you get

without combining terms

[last stone]

Oh nvm

The

5x/2

I thought it was gonna be 10x

[lapis vector]

oh no

[last stone]

But I already multiplied so 2 evaporated

[lapis vector]

yeah lol

is that all?

[last stone]

Ya little boy

[lapis vector]

[last stone]

quadratic equations are so easy lol

.close

[midnight plank]

Channel closed

Closed by @last stone

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[trim sun]

Ik how to find derivative but i just dont know how to deal with the exponents

[pale tartan]

Oh, well when we take dthe derivative of an exponent. We use the power rule.

If you could wait just one moment I’d like to make up some notes for it

Just to make sure. You want help with taking the derivative of an exponent right?

[trim sun]

Well if you could walk me through the problem that would be really helpful 😢

[scenic wyvern]

hi, just to remind you to avoid sending a full solution

[pale tartan]

Ok, I will do my best!

[scenic wyvern]

just in case

[pale tartan]

Hows about step by step shtuff?

[scenic wyvern]

as long as it's not all the way to the solution

[pale tartan]

Hmm, are examples of the same wuestion with different numbers good?

[scenic wyvern]

that's alright!

[pale tartan]

Alr here I go

[trim sun]

[pale tartan]

Here are the basics to the Power rule

If we take example C) into account. I think that could especially jelp you in this scenario, please ask me if you want some help interpreting the power rule to a fraction

[trim sun]

Ok im gonna try to figure it out and I’ll let you know if i get stuck

[pale tartan]

Alrighty, you know what the question is asking for in the answer when they mean Prime notation correct?

[trim sun]

Like f prime right

F’

[pale tartan]

Indeed

[trim sun]

Am i on the right track?

[pale tartan]

That is correct

Now the thing I’m having trouble understanding is what the question is asking for in terms of the numerator and the denominator itself…. I was only able to help you with the power rule

[trim sun]

Yeah i dont really know how to simplify from here cause like she probably doesn’t want me to actually calculate it to the 6th power righr??? 😭

[pale tartan]

Yeah, she wants you to simplify it to the point where the denominator has an exponent of 6

And where the Numerator is variable adding to each other, no exponent or anything (if I understand)

[trim sun]

Erm how do i do that 😭

[pale tartan]

I should’ve asked, what class are you taking.. because I saw derivative and jumped in without a second thought 😔

[trim sun]

Calculus

[pale tartan]

I actually don’t know how to solve the question it seems. I only know how to take the derivative of this here fraction

And well, your written answer was correct

I’m currently taking business calculus myself but I never got to a point where we made these kind of simplifications that Added to the exponent after taking the prime of the function

[trim sun]

Okay 💔

[pale tartan]

I apologise. Only thing I could provide was the power rule

[trim sun]

Im gonna ask for help again if thats alright with you ❤️

[pale tartan]

Please, anything I can do to make up I will do what I can twin

[trim sun]

I appreciate your help

Erm

I do have this other problem

[pale tartan]

Alright, this could be arranged I believe All you really have to do is simplify then add similar terms to where you’re left wit

2 fractions adding or subtracting frm each other

[trim sun]

Like that or am i completely off? 😭

[pale tartan]

Can you take the derivative of each variable in your question ising these notes

Then we can continue the next step

Is it me or is the picture blurry, should I send it again?

[trim sun]

? 😀

[pale tartan]

Wait, you are on the right track

[trim sun]

Yasss

[pale tartan]

But how can we simplyfy this further, what would multiply the 7 with specifically??

If you want me to rephrase i could do so

[trim sun]

7/1 so it would be 7/5?

7/2 not 5 😛

[pale tartan]

Indeed, you multiply the 7 by whatever’s on the Numerator. Which in this case would always be 1

I didnt even have to remind you of the power rule, you’re already cooking with the chain rule

Chain rule just being multiple rules being used in an order

[trim sun]

Did i cook

[pale tartan]

The third and fourth simplification is a bit wrong

[trim sun]

Is it negative

[pale tartan]

Yep

But actually, if upu already know upu’re going to be subtracting that positive answer you got. Its not necessarily wrong. Whichever’s more comfy for you

Would you like me to show you what I mean

[trim sun]

Is this like correct or am i making it up

Ignore negative mext to 6

[pale tartan]

Olr olr

But the answer wouldn’t be 6

[trim sun]

Would it he zero

[pale tartan]

Yep

[trim sun]

But then wouldnt it not work?

[pale tartan]

Hmm you’re right

Just one sec, could you show me your addition of the derivatives

Like how you wrote them after taking their derivatives. Seeing the steps could help me point summ out

[pale tartan]

Ahh now I got it

See, the denominators just do not work

[trim sun]

Ohh

[pale tartan]

In your question’s case. Since one denominator could never equal the other through normal means (multiplying with one variable)

[trim sun]

So i multipke 7/2x by 2 so its 4x and then -3 by 1/5?

[pale tartan]

Naurr, hold up now. My example is a bit bare bones and NOT suited for the question at hand actually

[trim sun]

Okkk

I think i got it now thanksss

Im going to bed i really appreciate your help 🥹

[pale tartan]

Wait, could you show me a final answer?

[trim sun]

If its wrong i already submitted it 😭

[pale tartan]

Oof

So, i think I didnt emphasicze that whatever you multiply the denominator by, you also multiply the numerator by for this situation

You go to bed and maybe check this answer ima give you like tomorrow

[trim sun]

Okay 😭

[pale tartan]

okay... So I went over the question proper, and I don't think you even got the part 1 question right, It's asking for all the variables to have an exponent of 1 which you don't have. and this is similar to the last question... which alludes to me accidentally wasting your time

I'm so fucking sorry

i'm just going to leave, the shame is simply too great

[midnight plank]

@trim sun Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[viral dagger]

$ABC$ is an acute triangle with $D$ being on $AB$. Find the location of $E$ and $F$ on $BC$ and $CA$ respectively such that the perimiter of $DEF$ is at the minimum

[grand pond]

ihave<skissue>

[viral dagger]

WLOG AC>BC, i hypothesize that the perimiter of DEF is at its minimum when F'F'_1 passes trough D and E

this

basically i mirrored F to BC and AB so that EF=EF' and DF=DF'_1

im not sure how to actually finish this tho

E can freely move around without affecting F'F'_1

so E would ideally be either trough F'_1D or on DF' (not sure which one is better)

im hoping i can somehow use this on D aswell? but unless its symmetric and im silly i dont know how to

[bold peak]

I have a feeling that coordinate bash might come into the picture here

[bold peak]

How about mirroring D instead? And then using those images to construct E and F?

[viral dagger]

oh right i forgot topic is "strategies for drawing"

[bold peak]

That tells me absolutely nothing lol

[viral dagger]

bruh

oh wait its not that trivial yet

oh it is...

[bold peak]

I'm just throwing out ideas

[bold peak]

Here's what I'm thinking

[viral dagger]

i mean its pretty obvious now isnt it

[bold peak]

Is it

I was thinking reflect the reflection

Anyway class starts now bai

[viral dagger]

perimiter of DEF is D'E+EF+FD'_1, which is something something triangle ineq >=D'D'_1, equality at E and F on D'D'_1

okay tyy

.solved

[midnight plank]

Channel closed

Closed by @viral dagger

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[drowsy turtle]

Can someone help me in these question !

[drowsy turtle]

If minus (-) sign is Thier so than I gonna take skew symmetric ?

Question 5 and 6

[midnight plank]

@drowsy turtle Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[drowsy turtle]

Not

[midnight plank]

@drowsy turtle Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[edgy crater]

im not sure if ive done this right, i equated both functions, and there established there would only be intersections if the discriminant was >=0, which led me to a quadratic in c, we need this to have real roots (discrimant >= 0) for the previous discriminant to have real roots, but i found this is true is mod a < 1, but in the q mod a > 1? probably done some things wrong thanks

[midnight plank]

@edgy crater Has your question been resolved?

[small jasper]

setting this discriminant to be positive makes no sense

since that allows for your $4c^2+(4a+8)c+(4a^2+4a+1)$ to be negative

[grand pond]

Civil Service Pigeon

[small jasper]

which would mean that $f(x)=x+c$ would have no solutions in the reals

[grand pond]

Civil Service Pigeon

[midnight plank]

@edgy crater Has your question been resolved?

[edgy crater]

oh yh tysm

.close

[midnight plank]

Channel closed

Closed by @edgy crater

Use .reopen if this was a mistake.

[small jasper]

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lyric charm]

!status

[midnight plank]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@median fossil Has your question been resolved?

[median fossil]

I cant figure out the r and h for cylinder B

[solid dawn]

i think that this year i'll be coocked

[surreal moon]

!occupied

[midnight plank]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[midnight plank]

@median fossil Has your question been resolved?

[small jasper]

(scale factor)^3 = ratio of volumes

[https://flexbooks.ck12.org/cbook/ck-12-basic-geometry-concepts/section/11.9/primary/lesson/area-and-volume-of-similar-solids-bsc-geom/]

[median fossil]

.close

[midnight plank]

Channel closed

Closed by @median fossil

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[meager ore]

If $R$ is a ring with unit element. Then every proper ideal is contained in a maximal ideal

[grand pond]

Halex

[midnight plank]

@meager ore Has your question been resolved?

Channel closed

Closed by @meager ore

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[edgy crater]

is this right, i feel like i may have made some incorrect assumptions, thanks🙂

[edgy crater]

2nd and 3rd lines refer to the last digit oops

[sacred folio]

too make it more refined you can say since x should end in 1 it could be of the form 10k+1 = x

then x^3 = (10k+1)^3

open the cube and ignore all the terms with 10^2 or above factors

so you get it's last two digits as 30k+1 where k is a positive integer

so 30k+1 = 11 or k =1/3 which isnt possible

so no case so probability is 0

[edgy crater]

ok tysm

[sacred folio]

[edgy crater]

but couldn't it also be like a x 10^3 + b x 10^2 + c x 10 + 1 but ig we dont rly care about the hundreds and thousands term etc

[sacred folio]

ye but ts way you get a possible case of 11 when c=1

when c has a definite value of 3

[sacred folio]

plus you have to reason why you have given ts expression in the first place

[edgy crater]

does ts mean this

[sacred folio]

yes

[edgy crater]

alr

[sacred folio]

I have a minor amount of brain rot due you ig so i tend to write words in short form to save time to waste it later

[sacred folio]

.close if you have no other doubts

[edgy crater]

.close

[midnight plank]

Channel closed

Closed by @edgy crater

Use .reopen if this was a mistake.

[edgy crater]

.reopen

[midnight plank]

✅ Original question: #help-49 message

[sacred folio]

[edgy crater]

doesn't k = 7 work

[sacred folio]

ts was our last expression

so putting k as 7 would give us 211

which isnt equal to 11

[edgy crater]

but ends in 11

[sacred folio]

hmm

[edgy crater]

sorry the q was that the cube ends in 11

but i think that just means k = 7

we want all numbers ending in 71

i think

[sacred folio]

ye

no no your right

mb

so 30k+1

lets start from ts

we need to find no. k such that the last digits are 11

[edgy crater]

i think it rly is just k=7

[sacred folio]

no no

lets try and simplify ts

[edgy crater]

so we want numbers in the form kkkkk71, so 10^5 possiblities?

ok

[sacred folio]

30k+1 = 100a + 10 + 1

30k = 100a + 10

3k = 10a + 1

[edgy crater]

11, 21, 31, 41, 51, 61, 71, 81, 91, only 21 divisible by 3?

[sacred folio]

so basically we have to choose a k such that when multiplied by 3 last digit is 1

[edgy crater]

yea

[sacred folio]

so any number that ends with 7

can be a k

[sacred folio]

so we need to find the total number of numbers btw 1 to 1000000 that end in 71

no wait

[edgy crater]

71 right not 7?

[sacred folio]

ye

[edgy crater]

yh so 10^5 i think

cuz like theres 10 possibilities for each slot apart from the ones filled by 71

[sacred folio]

first digit cant be 0

no wait it can

ye

10^5

[edgy crater]

yea nice yippee

ty

.close

[midnight plank]

Channel closed

Closed by @edgy crater

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[meager ore]

If $R = \mathbb{Z}[i]$. Show $I = \langle 5 \rangle$ is not maximal ideal in $R$

[grand pond]

Halex

[meager ore]

It is contained in $\langle 2+i \rangle$ which is maximal but not sure how to show it is maximal

[grand pond]

Halex

[raven ferry]

You don't need to show that it is maximal, you just need to show that it is not the entire set, making the previous ideal also not the entire set

uh

making the previous ideal not maximal

[meager ore]

I need to show it's maximal 😭

[raven ferry]

I meant that you just need to show that $\langle{2+i}\rangle \neq \mathbb{Z}[i]$, and that $\langle{5}\rangle \subsetneq \langle{2+i}\rangle$

[grand pond]

Feltheshovel

[raven ferry]

This would mean that $\langle{5}\rangle$ is contained in another proper ideal, which by definition, means that it is not maximal (I assume this is your definition for maximal ideal?)

[grand pond]

Feltheshovel

[eternal pawn]

||2+i||^2 = 5 which is a prime number...

[midnight plank]

@meager ore Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[coral belfry]

Hello. Is it easy for sb to explain what an ambient vector space is? If yes, explain as plainly as possible, i just wanna have an idea. I watched a vid abt a 3d surface within an ambient vector space

[subtle blaze]

What do you mean ambient vector space

[coral belfry]

i acc think the guy said field not space

he explained it as like a bunch of vectors flowing through our surface or on it

[subtle blaze]

Do you have a reference to “the guy”

[coral belfry]

hahah hes steve brunton on yt

[subtle blaze]

Do you have a specific video you’re referring to

And a timestamp

[coral belfry]

Stokes' theorem

lemme see abt the time

[subtle blaze]

Can you link it

[coral belfry]

3:04

[quartz vale]

an ambient vector field is basically a "wind" or flow of arrows defined everywhere in the surrounding 3d space (the "ambient" space) that contains your surface

so the surface is just sitting inside this bigger field of directions and speeds, like a boat bobbing in a river current that flows all around and through it

[runic hamlet]

it could just mean "the space you are currently working in"

[subtle blaze]

@quartz vale nice name for this question lmao

[quartz vale]

very poignant i know ;)

[coral belfry]

we use the curl of the vectors on the surface to compute integrals so i dont think it just exists in there, maybe it is affected by being in there too idk

[coral belfry]

that makes sense i think

[quartz vale]

bot work!!!!

[subtle blaze]

Don’t have spaces before the closing $

[grand pond]

∫_M dω = ∫_∂M ω

[coral belfry]

hmm that sounds good enough

[subtle blaze]

This is not explaining is simply tbh lol

[quartz vale]

yeah that was a more rigorous definition

[coral belfry]

Is T something like a linear operand or smth

at TR^n

[quartz vale]

tangent bundle

[coral belfry]

oh never heard of that

[subtle blaze]

No it’s the tangent bundle, which is a pretty complicated construction

[coral belfry]

i see

well thanks for the explanations. i appreciate the complex version too

.solved

[midnight plank]

Channel closed

Closed by @coral belfry

Use .reopen if this was a mistake.

[ruby nimbus]

hello

what is the question where can i find problems that you guys working on it?

[wet pollen]

Huh?

!help

[midnight plank]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[shut canyon]

How to find with ε-δ?

[shut canyon]

I see x goes to ∞, so maybe ε-N is better to be used

ε>0, ∃N,

when x≥N

so for sufficiently large x this function converges to some value?

lim(a/b)=lim(a)/lim(b)

[solid iris]

ε is for providing a direct proof of a limit once it is known, not for computing a limit

[shut canyon]

🐈

always?

[solid iris]

yes

[shut canyon]

x⟶∞, (cos x² - 1) ⟶ …
cos x² oscillates ∈ [−1, 1], cos x² − 1 ∈ [−2, 0]; no limit exists

[solid iris]

u forgot about x^2 below

[shut canyon]

x² is easy, perhaps goes to ∞

[solid iris]

what does the ratio approach?

[shut canyon]

I don't yet know, how do you see that?

[solid iris]

compare the growth of cos x² − 1 and x²

[shut canyon]

I forgot the x^2 in cos x

cos x²−1 bounded ∈ [−2,0], x² → ∞ ⟹ x² ≫ ≫ cos x²−1

[solid iris]

so the ratio approaches what?

[shut canyon]

0

[solid iris]

yes

[shut canyon]

Thank you @solid iris

[solid iris]

np

[shut canyon]

∀ε>0, ∃N s.t. ∀x>N ⇒ |(cos x²−1)/x²−0|<ε.
Pick N>√(2/ε) ⇒ |…|≤2/x²<ε
Because |cos x²−1| ≤ 2 ⇒ |(cos x²−1)/x²| ≤ 2/x².
To make 2/x² < ε, need x² > 2/ε ⇒ x > √(2/ε).
So N = √(2/ε) ensures the ε-bound

ε–N shows: for any ε>0 pick N>√(2/ε) ⇒ |…|≤2/x²<ε, hence limit = 0.

[solid iris]

yes

[shut canyon]

This is not computing the limit via the epsilon delta definition?

I don't yet understand this

[solid iris]

look back on our convo

we computed the limit BEFORE proving it with epsilon

[shut canyon]

Oh 0 is plugged to the definition

thanks lots

[solid iris]

np!

[midnight plank]

@shut canyon Has your question been resolved?

[solid iris]

.close

[midnight plank]

Channel closed

Closed by @solid iris

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sour hull]

a question gave me an imaginary number, it's not supposed to

[sour hull]

I'll print it out:

so we're supposed to find the maximums and minimums of a function, and if it's increasing or decreasing analytically

for that we use the derivative

we're given the original function

$f(x) = \frac{4x - 2}{x^2 + 2}$

[grand pond]

ℕ∈ℝD ALERT: Gonçalo Gonçalves

[subtle blaze]

And what does your working look like

[sour hull]

what the derivative gave me was: $$f'(x) = \frac{4x^2 - 4x +8}{x^4 + 4x^2 + 4}$$

Which gives a negative binomial when we equal it to 0

[subtle blaze]

Use one dollar sign

Also use f’

[grand pond]

ℕ∈ℝD ALERT: Gonçalo Gonçalves

[sour hull]

sorry typos

[subtle blaze]

,w d/dx (4x-2)/(x² + 2)

[grand pond]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by frosst

[sour hull]

yea

[subtle blaze]

Bad algebra

Check again

[sour hull]

there is a minus sign missing somewhere, let me check

[subtle blaze]

Yes

[sour hull]

actually nah I missed an exponent, anywho, let me do the binomail again

alright, the binomial is an integer, now let me just complete and check the solution

[midnight plank]

@sour hull Has your question been resolved?

[sour hull]

alright

.close

[midnight plank]

Channel closed

Closed by @sour hull

Use .reopen if this was a mistake.

[sour hull]

thanks @subtle blaze

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[inland patio]

The above screenshot lists three conditions necessary for differentiating a function under the integral sign (there are other, stronger conditions too). I'd like to verify the conditions (i) to (iii) for the function $$f(u,x)=\exp\left(-\frac{1}{2}\left(\frac{u^{2}}{x^{2}}+x^{2}\right)\right),$$ where we integrate over $E=\mathbb{R}$ and $I=\mathbb{R}$. Condition (ii) is obvious as $f$ with fixed $x$ is a smooth function. But I struggle with (i) and (iii).

[grand pond]

psie

[midnight plank]

@inland patio Has your question been resolved?

[inland patio]

By the way, I meant E = (0, inf) and I = R.

[midnight plank]

@inland patio Has your question been resolved?

Channel closed

Closed by @inland patio

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[plush prism]

Lets say i want to solve the gauss integral and make the switch to polar. Can someone say why the following is intuitively wrong?

x = r cos
y = r sin
dx = cos dr - r sin dtheta
dy = sin dr + r cos dtheta
Now the wrong part i think
dxdy = just multiply them
Then we get stuff with dx^2 and dtheta^2 and also r(cos^2-sin^2)drdtheta

[midnight plank]

@plush prism Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[jade magnet]

how do i do Q1.ii

[jade magnet]

im confused on what they are asking

what do they mean by prove this result

it only happens for specific cases

idk

i dont understand what the question is saying

its probably easy once i understand it

[robust isle]

Well it's not just for specific cases, they want you to show that for any invertible T and for any (x,y) invariant under T

[jade magnet]

oh

so if its invariant for the inverse transformation than its invariant for the transformation itself

thats what they want me to prove?

[robust isle]

Well the other way (not like it matters much really)

[jade magnet]

so i should let T = a matrix of say a, b, c, d

and then show what the inverse of T would look like

[lyric charm]

they want you to show that if $T \bmqty{x\y} = \bmqty{x\y}$ then $T^{-1}\bmqty{x\y} = \bmqty{x\y}$

[grand pond]

Ann

[lyric charm]

which is in fact a one-liner

[jade magnet]

oh ok

[lyric charm]

(unless you like making your own life difficult)

[jade magnet]

yeah so thats overcomplicating

[robust isle]

And yeah you can't assume T is 2x2 anyway

[jade magnet]

all i need to say is T-1 * T * (x,y) = (x,y) = T(x,y) = T-1(x,y)

[jade magnet]

yeah

ok

mb yeah this is pretty easu

easy

.solved

[midnight plank]

Channel closed

Closed by @jade magnet

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[grand stratus]

Prove that:
The sum of floor(log_2 ((2n/(2k-1)))) from k = 1 to k = n is equal to n.

[grand stratus]

I apologize for not being able to respond to my previous thread.

[pearl hull]

$\sum_{k=1}^{n} \log_{2}\left(\frac{2n}{2k-1}\right) = n$

Is this your question?

[grand pond]

e4 e5 Qh5 Nc6 Bc4 Nf6 Qxf7#

[lyric charm]

you forgor the floor

[grand stratus]

the expression being summed is floor(log_2 (2n/(2k-1)))

[pearl hull]

bruh

lemme test it out at #latex-testing

$\sum_{k=1}^{n} \lfloor\log_{2}\left(\frac{2n}{2k-1}\right)\rfloor = n$

[grand pond]

e4 e5 Qh5 Nc6 Bc4 Nf6 Qxf7#

[pearl hull]

@grand stratus is this your question?

[midnight plank]

@grand stratus Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lyric charm]

!xy

[midnight plank]

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.

[shut canyon]

1. Write in English what property of a function does this express.
2. Give example of function which has this property and one that doesn't.
   f : ℝ ⟶ ℝ

[lyric charm]

oh so your job is to translate that mess of epsilons into English

[hasty moss]

are u in neighbourhood of 1 or something

for all L in real and e greater than 0 and lets take del to be small and +ve idk about {1} it is saying |limit of f(x) in neighbourhood of 1 -L|]>e

ig

[shut canyon]

∀ L ∃ ε ∀ δ ∃ x ( |f(x)-L| ≥ ε )

[hasty moss]

it looks like greek now ngl

[shut canyon]

(…) \ {1} 1 is not in the delta neighbourhood of 1

[hasty moss]

ohh

[robust isle]

hint : negate that statement, what do you get ?

[shut canyon]

¬∀ L ∃ ε ∀ δ ∃ x ( |f(x)-L| ≥ ε ) ≡
∃ L ∀ ε ∃ δ ∀ x ( |f(x)-L| < ε )

[robust isle]

Yeah

Sounds familiar ?

[shut canyon]

Wow that's the epsilon delta

[shut canyon]

🎉 Thanks

f(x) converges to L as x→a

f(x)=x² has this property, because it is continuous, so when x is close to a, x² is close to a²:
∀ε>0 ∃δ>0 ⇒ |x−a|<δ → |x²−a²|<ε

construct δ:
|x²−a²|=|x−a||x+a|;
if |x−a|<1 ⇒ |x+a|<|a|+1,
so pick δ=ε/(|a|+1).

g(x)=1/x (x→0) does not have this property, as when x→0, 1/x diverges.

x→0, 1/x has no finite limit:

• from the right (x→0⁺) → +∞
• from the left (x→0⁻) → −∞
  No single L fits ∃L∀ε… ⇒ fails the convergence property

[grand stratus]

yes

[pearl hull]

Claim another channel

[paper mantle]

math wording is beautiful

holy

[shut canyon]

Cheers 🐬

[paper mantle]

btw what does the upside down A and E turned to the left mean? i always forget

[shut canyon]

∀ is for all ~ All

∃ Exists

[paper mantle]

thx

[midnight plank]

@shut canyon Has your question been resolved?

[sacred folio]

ts the worst topic in calculus 1 fr

wdym i need to prove the limit

[shut canyon]

I quite like it, it is challenging but seems to make sense after a while.
I'm still struggling though.
Maybe it is easier to start with convergence of sequences:

[autumn canopy]

What are you having problems with right now?

[shut canyon]

algebraic manipulations, seeing patterns, and proving the limit transforming the |…| inequality expressions

[autumn canopy]

Is it still about this?

[shut canyon]

for example maybe 1/(2x) < ε → x > 1/(2ε)

[shut canyon]

No, this I understand

[sacred folio]

too tedious for me tbh

i get it's purpose but i dont like it's existence

yfm

[shut canyon]

It teaches logic also for other mathematics patterns

[sacred folio]

the cons outweigh the pros for me

not like i have a choice anyway though

[shut canyon]

Reframe

[shut canyon]

topology generalizes ε–δ

[shut canyon]

You can find pros with mindfulness, and learn anything with growth mindset! 🌿

[sacred folio]

[midnight plank]

@shut canyon Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dawn dagger]

Question: \
If I have a tuple of numbers $(1,2,3,4)$ for example and now $1\mapsto 4$, $2\mapsto 3$, $3\mapsto 2$ and $4 \mapsto 1$ such that I get $(4,3,2,1)$ (alike to rotating the tuple (1,2,3,4) in 3D horizontally), is there a specific term for what I did? I have heard of involution or that it has to do with symmetric groups, but I am not quiet sure...

[grim vector]

Like permutation group ?

[dawn dagger]

yea

[grim vector]

I think you can write your transformation as a permutation

[hard umbra]

what did you do to it

flip it around?

[dawn dagger]

yes

like a set of cards

[grim vector]

List.rev

[dawn dagger]

and i think it's an involution because if i flip them again, then i am back at where i started

[hard umbra]

but there are tons of other involutions

just call it reversing the tuple?

nothing better than the most specific name

[dawn dagger]

oh okay

[grim vector]

cuz you can write it as a product of transposition (swap middle and swap extreme point)

[dawn dagger]

okay thanks guys

.solved

[midnight plank]

Channel closed

Closed by @dawn dagger

Use .reopen if this was a mistake.

[tight plaza]

Multiplied it with an exchange matrix?

ah shit, too late

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sour hull]

Considering the polinomial family $P(x) = x^{2n} + 2x^n + 1, with n \in N$. I want to show that, if $n$ is not pair, then P(x) is divisible by $x+1$

[sour hull]

to solve this

I am

[grand pond]

ℕ∈ℝD ALERT: Gonçalo Gonçalves

[sour hull]

using P(x) = (x+1) Q(x) + 0

and then

$x^{2n} + 2x^n + 1 = (x+1) Q(x) + 0$

[grand pond]

ℕ∈ℝD ALERT: Gonçalo Gonçalves

[autumn canopy]

What does "n is not pair" mean

[wanton belfry]

probably means odd

[sour hull]

oh yea

I didn't remember the name

so I just translated it to is not pair

but the right word is odd

it's correct

I remember now

[civic gazelle]

is x = -1 a root of P(x) then?

[sour hull]

well, I guess

how does that help?

[autumn canopy]

Then you are done

[sour hull]

?

[autumn canopy]

If a is a root of the polynomial p, then x - a | p

[civic gazelle]

little Bezout's theorem

[sour hull]

I never heard of that rule

[wanton belfry]

isn't it just euclidean division

[sour hull]

sorry

[sour hull]

what are these names you're spouting

https://tenor.com/view/information-overload-mind-blown-shouting-screaming-gif-15213853

[wanton belfry]

what are the theorems you know about polynomials

do you know any

[sour hull]

ruffini's law

umm

teorem of the rest (literally translating)

intire division

[wanton belfry]

yes use that

[sour hull]

hold it let me check other pages of the unit

[autumn canopy]

Let $p$ be an $n$'th degree polynomial and $a$ a zero. We can divide $p$ by $x - a$ and get [p = (x-a)q + r] for some polynomials $q, r$ with $\text{deg}(r) < \text{deg}(x - a) = 1$.

This is division with remainder, you agree with this?

We didn't use at all that a is a zero

This is just plain division with remainder

[autumn canopy]

This is good

Should be what I used

[sour hull]

well, ok, but I still don't see how it helps solve something to the nth power.

[grand pond]

Kepe

[autumn canopy]

It will help in a second

[grand pond]

Kepe

Kepe

Kepe

[autumn canopy]

So now you just need to check if -1 is a root, because by what we proved, it implies x - (-1) = x + 1 divides p

[sour hull]

ok calm down (me)

are all exam questions going to be like this?

[autumn canopy]

You probably already proved this in class or somewhere in your book

You maybe wouldn't have had to reprove it yourself

The only thing you need to do is plug in -1

And check if it's 0

[sour hull]

some questions before we move on

why divide $p$ by $x-a$, is p not $= (x-a)q + r$ by nature

[grand pond]

ℕ∈ℝD ALERT: Gonçalo Gonçalves

[sour hull]

?

like

from intire division

I said I understood but I rered it and noticed that

[autumn canopy]

Yes it is

What we show is that r = 0

[sour hull]

I see, we do the intire division of the polinomial we have by x - a, and it gives us r = 0

[near cliff]

i literally just told you that rule like an hour ago

[sour hull]

the only rules were then chain rule and that other rule

$f(\frac{b}{a})$

[magic kestrel]

Okii, sorry

[sour hull]

and

[grand pond]

ℕ∈ℝD ALERT: Gonçalo Gonçalves

[sour hull]

an hour ago that's it

[near cliff]

yes you can use that one i told you just now (it's called the remainder theorem) to prove what he just said

[autumn canopy]

all good, it's just a server mechanic, you can claim your own channel

[sour hull]

I get what you're saying, but i saw something to the power of n and I got scared

[near cliff]

all good

[sour hull]

it's this part

[autumn canopy]

Yep, the remainder r is always 0 when a is a zero of p, as we proved

[sour hull]

right, I saw your deducation, I still don't understand how if the number was odd it is divisible by x+1. Is it because it works on every number?

[autumn canopy]

As we just proved, if a is a zero of p, then x - a divides p.

We want to prove that x + 1 divides p, right?

And so it's enough to show that -1 is a zero of p

And now you plug -1 into whatever your p is

And see if it gives you 0