help-26

[neon iron]

ah ok

great!

ok but now, i have an issue

because i get $\dfrac{\cos(6x^2)}{x^2} = \sum_{n=0}^\infty (-1)^n \dfrac{6^{2n} \cdot x^{4n-2}}{(2n)!}$

[thorny flame]

Derivative

[neon iron]

now if i subtract by 1/x^2 how will i incorporate this into the sum?

[vernal matrix]

Naughty

Anyways, consider how the actual summation you have looks like...

[neon iron]

i dont know

i just did what i could hahah

did i invent math rules?

🤣

that happens to me when im lost hahahah

[vernal matrix]

Well, I mean, I'm just being fussy

[vernal matrix]

But, anyways, write out the first few terms of what you have

[neon iron]

ah the 1/x^2 cancels

thats great

and then i find the 10th term

?

[vernal matrix]

Yep

[neon iron]

alright let me try

[vernal matrix]

(but be a bit careful, it's a bit confusing )

(In particular, the term corresponding to the coefficient of x^10)

[neon iron]

ok

do i make a new series after i cancel out the -1/x^2

[vernal matrix]

You could, or write what you'd basically find $\sum_{n = 1}^{\infty} (-1)^n\frac{6^{2n} \cdot x^{4n - 2}}{(2n)!}$ and see what the $x^{10}$ term's coefficient must be (or just write out the first few terms, shouldn't take too long)

[neon iron]

isnt it 6^2*10

the 10th coeficient

n=10

[vernal matrix]

Not quite, you want x^10, and n = 10 would give you x^38

[neon iron]

ah ok

n=3 then

ok

but here is my question

my series does look ugly

how do i make it look nicer

[thorny flame]

@vernal matrix

[neon iron]

like you are right the x^4n-2 is pretty ugly

but anyway if there is no other way so be it hahah

[vernal matrix]

Not that much you can really do that'd make it any nicer

[neon iron]

so my answer should be -6^2*3

its wrong for some reason

i must have got the series wrong then

[vernal matrix]

Actually wait a moment

Ideally we should have something that's close to the "standard form" when you're centred about 0, the whole $\sum_k \frac{f^{(k)}(0)}{k!} x^k$, but here it's a bit messier as the power and factorial don't quite match up

[thorny flame]

@vernal matrix

[neon iron]

yes

so there must be a way to simplify it

[raven field]

just a question what is the first term of the Taylor expansion of cos(6x)

[neon iron]

i used the taylor exapsnion of cos(x)

and then did cos(6x^2)

and plugged in 6x^2 into x

[raven field]

But the first term is 1 right ?

[vernal matrix]

I'd think to just write out the x^10 term and work with it to get it in the right form

[neon iron]

yes

[vernal matrix]

In particular, it works out as $-6^6 \frac{x^{10}}{6!}$, and if we can make that denominator $10!$, we're happy

[thorny flame]

@vernal matrix

[raven field]

Ok so the numerator will be
(1+x^2/2!-x^4/4!….)-1

[neon iron]

ah ok

but i need cos(6x^2)tho

because thats part of the function

then i divide by x^2

and subtract by 1/x^2 to get the taylor expansion of f(x)

[raven field]

How about expanding it like this

[vernal matrix]

Still get the "not in correct form" thing

Hence my suggestion to write the x^10 term out and manipulate it to be in the right form

[raven field]

but doesn’t all the terms now divide by x^2 and when x=0 all terms are zero

[vernal matrix]

I think you're misunderstanding what the question wants

They want the tenth derivative, which is effectively "the stuff that multiplies x^10/10!"

[neon iron]

ah ok

i thought it was n=10

f^n(0)

but yes

[neon iron]

so what would be the x^10 term though

thats the problem

[raven field]

ohhhhh I reread the question sorry for the mistakes

[vernal matrix]

The $x^{10}$ term is $-6^6 \frac{x^{10}}{6!}$, but notice the denominator is $6!$ rather than $10!$

[thorny flame]

@vernal matrix

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[topaz sinew]

@subtle gulch Has your question been resolved?

[topaz sinew]

@subtle gulch Has your question been resolved?

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[subtle gulch]

.close

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[broken matrix]

can someone tell me why in convolution when we shift the h(t) like integral f(τ)*h(t-τ) dt , why dont we substitute in the "delayed value" ?

[sweet shard]

What are you even asking

What substitution are you even talking about

[vestal sigil]

we prefer leaving it as t and vary it from -oo to +oo

[broken matrix]

the delayed - shifted value of h(t) over x(t)

[vestal sigil]

and wherever theres ovrlapping, you integrate

to find the response of the system

[broken matrix]

why

but how the function gonna have the right values?

[vestal sigil]

because before you evaluate the integral on a certain overlapping interval

you substitute h(t-τ) by the expression of the function in that interval!

its not always the same, it may differ depending on interval

also, when you shift by t0, it becomes h(t0 - τ) right

so youre only finding y(t0) ?

we want to determine the whole signal y(t)

not just one value of it!

[broken matrix]

and how

[vestal sigil]

this is engineering, linear time-invariant systems 😛

[broken matrix]

it alter the signal

with delayed signal

after integration

@vestal sigil

that doesnt make any sense to me

[vestal sigil]

setting t=t0, gives you the value of y(t0) only

but we want the whole signal y(t)

its useless to set t=t0

we vary it from -oo to +oo

to have the value of y(t) for all t in R

[vestal sigil]

if youre ONLY interested in the response of the system at a certain time t0

then you can let t=t0

[broken matrix]

oke i got it

[vestal sigil]

but if you want to determine the entire signal y(t), for all t in R

[broken matrix]

thanks

but how

the h(t)

[vestal sigil]

im bad at explaining, hopefully you really got it 😛

[broken matrix]

is altered

for the shifted valued

@vestal sigil huh?

[vestal sigil]

if h(t)=sin(t) for example, it does not get altered

its always sin(t)

but if h(t) is a square wave for example, then for some intervals it will be +A and for other intervals it will be -A

you just gotta graphically shift h(τ)

and decide what to substitute for h(t-τ)

based on the overlapping interval

this stuff is hard to explain like this

[sweet shard]

Explains the non existent context

[vestal sigil]

video on YT is better

[vestal sigil]

lol

[topaz sinew]

@broken matrix Has your question been resolved?

Channel closed

Closed by @broken matrix

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[smoky musk]

need help

[smoky musk]

Translated: Solve the following Function for x

[sweet shard]

Uhhh probably change your username

[agile harness]

name is fire

[smoky musk]

cant

[sweet shard]

<@&268886789983436800> man needs help username change

[agile harness]

damn

[smoky musk]

I dont have the power to change it to "Big" or something like that

[agile harness]

why not

just hit edit profile

[sweet shard]

Skill issue

[smoky musk]

naw I dont want to actually change my name

Only for this server so I dont get trouble

[agile harness]

maybe they changed it for you

[smoky musk]

do you guys know how I can go about my problem?

[agile harness]

looks like angle sum

[smoky musk]

thanks for changing

[agile harness]

on the right

do you remember the formula for sin(u-v)

[bright trail]

If you want a particular nick I can give you it so long as it is sfw

[smoky musk]

yeah, the problem is that I have to calculate by hand so I can´t do anything fancy that requires a calc

[smoky musk]

Joe pls

[agile harness]

brother

$\sin(u-v) = \sin(u)\cos(v) - \cos(u)\sin(v)$

[thorny flame]

knief

[agile harness]

look familiar?

[smoky musk]

you mean sin(u−v)=sin(u)*cos(v)−cos(u)*sin(v) right?

yep

[agile harness]

yea exactly what i wrote

💀💀

[smoky musk]

💀

[agile harness]

🤦🏼‍♂️

do better man

[smoky musk]

sorry man

lemme see if it works

[agile harness]

apology accepted

[smoky musk]

one sec

first I have to simplify before using right?

[agile harness]

brother what

[sweet shard]

Use the identity knief told you on the right side

[sweet shard]

Of this

[smoky musk]

kk

almost there

Is this correct

[sweet shard]

Plug your angle in to the starting equation to check

[smoky musk]

Kk

[agile harness]

$\sin(\frac{\pi}{3}) = -\frac{\sqrt{3}}{2}$?

[thorny flame]

knief

[smoky musk]

ah so it´s correct

Lemme try anyways one sec

Got it thanks guys

.close

[topaz sinew]

Channel closed

Closed by @smoky musk

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[mild stratus]

a pleasant day to anyone there, I'm in real need of help with something

[mild stratus]

it's somewhat related to physics but certainly applies trig

I just wanna understand it better

got a project wherein we're trying to use a method of sound source localization with the use of two microphones

and I'm having a hard time understanding how the process yields the angle of the sound source

I have some ideas but I still can't quite grasp how the direction of the sound source could be found

https://stoppi-homemade-physics.de/richtungshoeren/

original link to the article

[vernal vale]

which part is giving you issues?

[mild stratus]

I don't understand the relation of the sin function to finding the sound source

where the specific angle is too

thx for the response btw

[vernal vale]

theres a lot in this diagram

Do you wanna go over it a little

or do you feel like you generally get the diagram

since it really kinda says it all

[mild stratus]

mhm, I would like a bit of an explanation, that would be nice

[vernal vale]

okay, so you understand those two red lines, theyre the sound, and they come from a single point

they move at the same speed, and the speed doesnt change, in this picture

[mild stratus]

alright

343m/s I take it?

[vernal vale]

this i think depends

the exact speed

[mild stratus]

mhm, on temp I believe

[vernal vale]

humidity and other stuff

[mild stratus]

mhm

[vernal vale]

but youre probably talking about a change in ... whatever 330 to 340

over a distance of whatever, 2 meters?

youll have more errors from latency than using the wrong constant

or idk i say that, id have to crunch the numbers

anyways

[vernal vale]

heres a different drawing of the same picture

so the blue lines connect the waves at certain points in time

just imagine the red lines as individual sound waves, and they leave the object at the same time, at the same speed

but in different directions

so the distance between them grows, but we can always draw a line between them at some instant in time, and these will always be parallel to other lines we could draw at some other time

good to there? @mild stratus

[mild stratus]

def worried 'bout that mhm

[mild stratus]

yep, so far so good

[vernal vale]

okay

one of these blue lines is in your other diagram

its the adjacent side to the marked alpha angle

so for some t value, both sound waves are at exactly the same place

lets call the left wave Wave 1, it's just hit the first microphone

but the right wave, Wave 2, is a little bit behind from hitting microphone 2

it takes a little bit longer, since the distance is a little longer, it actually takes t+ delta t to reach microphone 2

and in that time, it moves the final delta s remaining distance, from where it was just behind, to finally hitting the microphone 2

Thats almost the entire physical picture. The only other piece is to know that the tiny distance it traveled, delta s, is just the speed it was moving, multiplied by the time it spent traveling

@mild stratus physical picture good?

[mild stratus]

oop, sorry for the late reply, hold on

[mild stratus]

oh alright, that makes sense

[vernal vale]

okay

now you can tell me if you have problems with another picture

[mild stratus]

mhm

[vernal vale]

there is a tiny simplification were applying here, but you might not even notice/care

[mild stratus]

oh? alright

[vernal vale]

important parts here

we know d, in fact we can choose it by moving the microphones, so that's known

[mild stratus]

right

[vernal vale]

we "know" the speed of sound, and we are measuring delta t, so delta s is known

[mild stratus]

yep

[vernal vale]

now its just normal ol right triangle math

[thorny flame]

jan Niku

[vernal vale]

since SOH (cah toa)

and we're there

a more advanced geometry problem: Remember that the blue lines are only parallel to each other, and they are actually all different lengths

so where we drew a right angle, its actually a LITTLE bigger than 90 (how much bigger? what's the error we incur by assuming its only 90?)

but maybe for another day

[mild stratus]

oo woah

[mild stratus]

also question, could angle alpha there perhaps also act as the angle that points towards the sound source?

[vernal vale]

yea, and it's shown like this in your original drawing. It's just some basic complementary/supplementary angle line-drawing and angle-matching logic to get there

[mild stratus]

that is an interesting question lol

[vernal vale]

youll have to do some work

but not a lot

remember alpha picks up the error that you make in the 90 degree part

so that's going to track

but there's other errors as well

if you actually implement this and start getting crazy results that dont make sense

maybe thats the time to start doing some of this more crazy math

[vernal vale]

like here i think that Wave 1 makes an angle 90 + alpha with the wall?

so maybe you imagine that alpha to the left from a directly vertical line points to the sound source

like is drawn to the other side

[mild stratus]

oo I see, will have to review a bit on those, the idea I sorta have is that the angle of the sound source from mic 2 could be taken with "90°"-alpha

[vernal vale]

this seems like a fun project

hope you are successful

[mild stratus]

hope so too, thanks so much for your help

[vernal vale]

[mild stratus]

this problem has stunted me for days now and I couldn't find any sources on the Internet that tackled it in a simple way

much appreciated

[topaz sinew]

@mild stratus Has your question been resolved?

[mild stratus]

Yes

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[distant shadow]

Can anyone see where i went wrong in this partial derivitive question?

original function is $F(x,y)=-3x^{2}-6y^{2}+3xy=0$

[thorny flame]

epi

[gleaming reef]

it should be -F_x/F_y

no?

[distant shadow]

yeah i have that in other parts i just forgot to add it it when i was rewriting it for discord

oopsies

oh shit

at the end i missed it

that is correct thank you

<3

.close

[topaz sinew]

Channel closed

Closed by @distant shadow

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[safe mica]

does this check out?

can i use cos(s+t) to figure out what quadrant (s+t) is in

and so on for all trig functions of that expression

[mental trench]

what class is this?

just curious

[topaz sinew]

@safe mica Has your question been resolved?

[safe mica]

precal

[mental trench]

oh okay

can't you convert sin(s+t) into sin(s)cos(t) + cos(s)sin(t)?

[safe mica]

yeah thats what i did in the work

thats an identity

the result of sin(s+t) they want to know what quadrant is so i just figured if i did the identity for cos(s+t) it would work? and that would be sufficient enough to show it's quadrant 3 since the result of cos(s+t) is positive and since the result of sin(s+t) is negative it cant be quadrant 1 so maybe it must be 3

[mental trench]

yeah I think its Q3 too

[topaz sinew]

@safe mica Has your question been resolved?

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[quiet sorrel]

so i understand the solution, but i just want to clarify a few things:

1. is the conjugate of z in polar form always r*e^-iθ?
2. is r^2 = 1 always true in regards to complex numbers?

[quiet sorrel]

answer is 7 btw

[cursive patrol]

r^2 = 1 misses the point

r can be any real value, but e^(i angle) is what you know to have a magnitude of 1

(ans to ur first question is yes)

[quiet sorrel]

but how does that make r^2 = 1

[molten raven]

r=1 when r=/=0 by considering the magnitude

e^(6 i theta) always has magnitude 1 so r has magnitude 1 when it isn’t 0

[topaz sinew]

@quiet sorrel Has your question been resolved?

Channel closed

Closed by @quiet sorrel

Use .reopen if this was a mistake.

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[dusk raft]

do I deserve the mark

[somber socket]

No

Can’t say “shown in diagram” as an explanation ever lol

[hallow shuttle]

yup

[dusk raft]

@somber socket what should I have said

other than alternate angles

[somber socket]

Just that

[dusk raft]

😔

[somber socket]

You have to explain how to got 60

You just wrote 60 bc it worked

Didn’t actually say why it had to be 60

You can’t use the answer given to use to help justify

[dusk raft]

fair enough

thanks

.close

[topaz sinew]

Channel closed

Closed by @dusk raft

Use .reopen if this was a mistake.

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[royal sky]

what is it asking here?

[flint stump]

Every solution of the first system, when pre-multiplied by S, is a solution to the second system

the question asks you to prove that

[royal sky]

kk ty

.clise

.close

[topaz sinew]

Channel closed

Closed by @royal sky

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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 dove]

What have i done wrong here

[cunning kayak]

send ques

[trim dove]

I had a doubt in the log part

I think i got it wrong

[sudden temple]

where the logarithm disappeared

that's a mistake

[topaz sinew]

@trim dove Has your question been resolved?

Channel closed

Closed by @trim dove

Use .reopen if this was a mistake.

[trim dove]

.close

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[visual monolith]

Hi I have a question about checking work for antiderivatives, so I have the equation f(x)=(x^2)/4 +1 so the general antiderivative would be F(x)=(x^3)/12+x+C

I am a bit confused on how to check the answer for F(x)

[pseudo sonnet]

differentiate it

you should get back f(x)

F'(x) = f(x)

[visual monolith]

i see

thanks

.solved

[topaz sinew]

Channel closed

Closed by @visual monolith

Use .reopen if this was a mistake.

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[clear scroll]

can I carryout an anova analysis if my variable are not correlated.

[topaz sinew]

@clear scroll Has your question been resolved?

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[clear scroll]

no...

[topaz sinew]

@clear scroll Has your question been resolved?

[outer salmon]

.close

[topaz sinew]

Channel closed

Closed by @outer salmon

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[elfin niche]

How do you solve for x :

[elfin niche]

$2log_{2}X - log_{2}(x+3) = 2$

[thorny flame]

Beersathought

[elfin niche]

so what I done :

$log_{2}\frac{x^2}{x+3} = 2$

[thorny flame]

Beersathought

[elfin niche]

Not sure where to go on from there though

[restive inlet]

raise 2 to the power of each side
(apply the definition of log / relation between exponents and log)

[elfin niche]

I also saw that explanation, but how does it work really?

u mean like
$2^{log_{2}\frac{x^2}{x+3}} = 2^{2}$

[thorny flame]

Beersathought

[elfin niche]

right?

Which makes

$a^{log_{a}X} = X$

[restive inlet]

yeh

[thorny flame]

Beersathought

[elfin niche]

is there no other way than this?

[restive inlet]

not really, no

[elfin niche]

Hmm I see

What about

$log X - log(x-4) = log 12$

[thorny flame]

Beersathought

[elfin niche]

I know that base is 10

so

[restive inlet]

same idea

base^(power of each side)

[elfin niche]

$10^{log_{10}\frac{X}{x-4}} = 10^{log_{10}12}$

woops

[thorny flame]

Beersathought

[elfin niche]

so always by the base?

[restive inlet]

yes

[elfin niche]

I see

But this is also

$log M = log N$

[thorny flame]

Beersathought

[elfin niche]

$M = N$

[thorny flame]

Beersathought

[elfin niche]

?

or this is wrong?

[restive inlet]

its fine

[elfin niche]

I see

Alrighty, thanks for that

Do have a good day

.close

[topaz sinew]

Channel closed

Closed by @elfin niche

Use .reopen if this was a mistake.

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[neon iron]

question about the minimal number of edges in a graph: at the beginning of the section they said that they assume G to be always a multi-graph that is connected. Here they are saying the minimal amount of edges for G are nk/2 for k being the minimal possible degree. but shouldn't the minimal number of edges in a connected graph be n-1 (a tree)? Correct me if I am wrong

[craggy haven]

I'm not sure what their μ is but in a tree the minimum degree is 1 (or 0 for degenerate cases)

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

sorry, forgot to metion that; μ is the size of the minimal cut

and sorry, I also noticed something just now; what i am specifically asking is what if minimal degree is 1? could we then even say |E| <= n-1, since a connected graph with minimal degree 1 has as least as many edges as a tree with n vertices?

when the graph also has n vertices ofc

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

.close

[topaz sinew]

Channel closed

Closed by @spare summit

Use .reopen if this was a mistake.

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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 widget]

find the general term

[karmic widget]

i got an answer but its not the right one

tn=2-(1/2)^(n-1)

[topaz sinew]

@karmic widget Has your question been resolved?

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[lusty cedar]

I need some help

so basically

I write it as an exponential to the power of a half

then I get 1/2(3-sin^2x)^-1/2 times the deravative of the inside which is -2cos x i think

so -1/2cos^2x(3-sin^2x)^-1/2

but this is the answer

[restive inlet]

times the deravative of the inside which is -2cos x i think
derivative is wrong
you forgot about the second application of chain rule for the derivative of sin^2(x)

[lusty cedar]

2sinxcox x

ah

damn

thanks

Im rly quite lost on this one

I tried bringing the power down

and deravative of the inside

isnt that 1/tanx x -cotx

well its sec^2 x apparently not cot x

tf

[static viper]

Wdym

Derivative of tan x?

[lusty cedar]

shit u have to use quotient to derive that

they give it in my formula booklet anyway

[static viper]

No

[lusty cedar]

yeah im not gna bother with that

ill j say sec^2 x times 1/tanx

[static viper]

Derivative of ln(tanx) = 1/tanx * derivative of (tanx)

[lusty cedar]

yeah i derived tanx wrong

I had gotten -4xsin(x^2+1)

by doing du/dx times dy/du

why is there still a cos^2(x^2+1)?

[topaz sinew]

@lusty cedar Has your question been resolved?

[restive inlet]

why is there still a cos^2(x^2+1)
there isn't

just cos(x^2+1)

similar to the previous questions, there are two applications of chain rule

from the first application you'll have
2cos(x^2+1) * d/dx (cos(x^2+1))

[topaz sinew]

@lusty cedar Has your question been resolved?

[lusty cedar]

Thanks

[topaz sinew]

Channel closed

Closed by @lusty cedar

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[reef field]

Hey there folks, if I could get some help walking through a question similar to this I would appreciate it.

[pseudo sonnet]

you need to find the points where g(x) has either an asymptote or a hole

those points will not be in the domain of g(x)

asymptotes occur when at points where we divide by 0 (without 0 in the numerator also), and holes occur at points where when plugging a number into g(x) gets you something looking like 0/0

so our job here is to find at what numbers we’ll be dividing by 0, or getting a hole

once we do that, we’ll know that the domain of g(x) is simply all of R minus those problematic numbers

now since we care about division by 0, a good first step to take is to examine which numbers make the denominator 0, which means setting it to 0 and solving for x

[barren ember]

I think the way to solve it should be via wavy curve method

[reef field]

Alright thanks guys👍

.close

[topaz sinew]

Channel closed

Closed by @reef field

Use .reopen if this was a mistake.

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[sleek prism]

@neon iron

[neon iron]

alright

omg

i got it

[sleek prism]

Fr?

Send pic

[neon iron]

yes

let me rearrange it

[sleek prism]

👍

[neon iron]

@sleek prism

[sleek prism]

Um

Explain pls

[neon iron]

${c = c_1 + c_2}$, no?

[thorny flame]

icannotdoanymorecauchy

[sleek prism]

Yeah i get it

The transformation

[neon iron]

so $c^2 = c_1^2 + 2c_1c_2 + c_2^2$

[sleek prism]

Am a little confused with the handwritting

[thorny flame]

icannotdoanymorecauchy

[sleek prism]

Yeah than?

Oh got it

Lemme read the rest

Rms gm?

Probbally idk the formula

[neon iron]

i was thinking abt cauchy-schwarz first bro

[sleek prism]

Nah this exercise aint for me

XD

Anyway

Thanks

🤝

[neon iron]

also

[neon iron]

u can prove this using right triangle too

maybe i overcomplicate

if u're interested:
https://youtu.be/_gTClIbHreI?si=yq9VrFWA9EpvMYYb

[sleek prism]

👍

Appriciate it

.close

[topaz sinew]

Channel closed

Closed by @sleek prism

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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 rose]

Why are there more reals between 0 and 1 than naturals?
Here's the explanation I heard:

Assign every real number a natural "index", like so:

0 - 0.123...
1 - 0.456...
2 - 0.999...

Then, make a new real number by taking the nth decimal of the nth real, adding 1, or making it a zero if it is a 9. So our new number would be 0.260..., and it's nowhere in the list.

The reason I don't understand that this as proof is the fact that we have an unending amount of naturals. Even when we come up with a new real number, can't we just come up with a new natural? Instead of doing it the way above, I could assign each real number between 0 and 1 an identical natural, except I remove the decimal point and increment the one's digit. So, 0.0123... has 10123.., 0 has 1, and 1 has 2. Another way I could do it is Hilbert's Hotel style. Increment every index and insert the new number created by diagonalization at the beginning.

[neon iron]

the thing is

there will always be at least one more new real number than the natural that u will come up with

[prisma mesa]

Infinitely many more in fact

[neon iron]

sorry

[shut rose]

And why is that? I just said in my question how you could deal with that new number.

[whole geode]

Not all decimals terminate

But all integers do

[prisma mesa]

Imagine that every single one of the infinitely many naturals is already matched with a real, then u cant come up with new natural

[whole geode]

No, Hilbert Hotel is valid method of dealing with it

[shut rose]

You're telling me something I already know. I want to know why it is that way.

[whole geode]

The idea is you can always generate more reals that you haven't accounted for. And if you start from the assumption that you've accounted for all of the reals already, then this is a contradiction

So your assumption (that there is an enumerable list of reals) is false

[burnt badger]

Well idk how to prove it rigorously but consider this

Let's say that for each natural number, that there are many cousins of that number as such:

For n = 1, let
.1
.01
.001
.0001
Etc etc

Be the "cousins" of 1

If you think of it this way

Just for the number 1

You'd have an infinite number of "cousins"

And that's only rational numbers too

[whole geode]

Which is wrong, because a bijection exists between rationals and integers

[shut rose]

But I can assign a natural for each new real

I said how in the question

[whole geode]

But you assumed that you already had a complete list

[prisma mesa]

Not really, because all naturals are already asigned.

[shut rose]

How so? There is an infinite amount of naturals. I can't assign all of them because there is always a bigger natural

[prisma mesa]

You can. E.g. f(n) = 1/n assigns each natural

[burnt badger]

Actually is this a countable vs uncountable question?

[shut rose]

That's the explanation I heard. Where you "imagine" you have a complete list but then you create a new number through the diagonalization method, but I just said how I could account for that new number

[prisma mesa]

you need to imagine that all of them are already matched

[hearty turret]

infinities gets a little confusing and so a lot of our intuitions don't carry over nicely

[prisma mesa]

yes, you cant write out a full infinite list, but you need to imagine that such list exists

[prisma mesa]

Are you familiar with functions?

[hearty turret]

but basically the argument is suppose that there were 'the same number' of real numbers between 0 and 1 and natural numbers

if there were, then you could tell me a list of how to pair them up:

i.e. 1 -> 0.001 etc. as u've done up there

[prisma mesa]

and that list would be complete. Every natural would get mapped

[hearty turret]

the fact that we can create a number not on the list means that it must be impossible to pair them up as i've described above

[shut rose]

But that assumes that all naturals are already assigned, but what about the hilbert hotel method? Or pairing them up like this: 0.001 -> 1001 (removing the decimal point and replacing 0 with 1). Whatever real I would create I could convert it to another natural

[burnt badger]

The irrational numbers specifically make this impossible

You can identify, in a systematic, countable way all the rationals between 0 and 1

[prisma mesa]

Assume that there is a bijective function f: N -> [0, 1].
So e.g.
f(1) = 0.123456789...
f(2) = 0.234567890...
f(3) = 0.531411433151....
etc...

Now you can do the trick, and come up with a number in [0, 1] that isn't in the range of f, and hence f can't be bijective.

[hearty turret]

ur pairing doesn't work cus 0.3333333... etc. isn't paired with anything

[burnt badger]

But how would you do that for irrational?

[hearty turret]

idk what u mean by the hilbert hotel method

[burnt badger]

Which is the first irrational number to start counting

[hearty turret]

but yeah we're assuming the naturals are already paired bcus we're doing a proof by contradiction

r u familiar with what a proof by contradiction is?

[shut rose]

If I have:
0 -> 0.123...
1 -> 0.456
And I come up with a new real, I increment the indexes and insert the new real at the beginning:
0 -> new real
1 -> 0.123...
2 -> 0.456...

I can always add 1 to a natural so I will never run out of indexes

[hearty turret]

right this is where our intuition doesn't carry over so nicely

because there's just too many real numbers

u'd never be able to fit them all

[shut rose]

I would because I can always increment a natural number

[prisma mesa]

The problem is that the 2nd list will be also incomplete

You are not thinking in terms of contradiction here

the proof is by contradiction

[shut rose]

I know but I would do this infinitely many times

[hearty turret]

^?

it feels like ur confusion is coming from here

[shut rose]

What is the contradiction

[prisma mesa]

You assume that there is a matching that's already perfect

meaning that for every number between 0 and 1, some natural already maps to it

but then you can do that diagonalization trick, and come up with a real number which isnt in the matching

and that's your contradiction

[hearty turret]

also there's a bit of an issue with 'do infinitely many times' here

[shut rose]

Yeah but I would just fit it into the list with the hilbert hotel method

[prisma mesa]

because you've shown that every perfect matching is actually imperfect

[prisma mesa]

I mean, sure, you can. But it will show nothing.

[hearty turret]

if you look at proofs that use 'do infinitely many times', it'll be with countable sets and u'll be doing it from the end

u're adding stuff to the end

but there's a problem with 'do infinitely many times' at the start

[prisma mesa]

The proof already shows that a perfect matching cannot exist. Yes, you can make it better by adding that 1 real number, but you wont get a perfect matching anyway

[hearty turret]

because you're saying we've got a bijection f that maps from N to [0,1]

[hearty turret]

u've defined it by doing a list like this, and then for any real that's missing you add it to the front

and then you do this infinitely many times for each missing real

but the problem here is that f(1) isn't defined now

[prisma mesa]

❓

what

[hearty turret]

as in with their hypothetical function f, they've constructed it by shifting it infinitely many times

but that's not well defined cus f(1) isn't really defined

[prisma mesa]

why would f(1) be undefined?

[hearty turret]

well like hypothetically what would it equal?

if i initially map f(n) = 1/n

[prisma mesa]

hypothetically, you cant just shift it for each missing real

[hearty turret]

and then i continuously add i.e. 1/(n+0.5) to the front

and i define f by doing this process infinitely many times

[prisma mesa]

there is no axiom / proof method in math that allows you to execute this step infinitely many times

[hearty turret]

then f(1) is no longer defined

[prisma mesa]

f(1) would be the "new real" number, wouldnt it?

[hearty turret]

each of f_1, f_2, f_3 (where f_1 = 1/n but with 1/1.5 shoved in at the front etc.) are well-defined but f_omega isn't

[hearty turret]

the thing is they want to do the process infinitely and f isn't really converging to anything here

[prisma mesa]

yeah, it's probably not

[hearty turret]

anyway that's another reason why their thing doesn't work

[prisma mesa]

uh

[hearty turret]

but yeah ^

[prisma mesa]

I'll just repost the proof here

Assume that there is a bijective function f: N -> [0, 1].
So e.g.
f(1) = 0.123456789...
f(2) = 0.234567890...
f(3) = 0.531411433151....
etc...

Now you can do the trick, and come up with a number in [0, 1] that isn't in the range of f, and hence f can't be bijective.

This proof shows that every perfect matching is missing some real.

Hence no perfect matching can exist

[shut rose]

Yeah but I can add it to the list...

I will never run out of natural numbers to assign to the reals

[vernal matrix]

But the thing is, you assumed you had everything in the list, that nothing was missing, but there will always be something missing

Even if you add it, there’s gonna be another thing you’re missing from the list

[hearty turret]

also i explained up there why ur method of adding to the list also doesn't work

cus you can't just repeat the process infinitely many times

[shut rose]

yeah didn't really get that

[hearty turret]

ok so maybe let's break this down to

there's the same number of positive integers and integers right?

how do u know that?

[shut rose]

Two sets have the same cardinality if I can make a one to one pairing for each item, which I can do with naturals and reals

Any real is just the last natural in the list + 1

I won't ever run out of naturals so I can always pair them

[hearty turret]

well ok the key thing here is that you can make a 1-to-1 pairing

[shut rose]

ok so same size

[hearty turret]

so can u provide me a proof of why the cardinality of N and Z are the same?

[shut rose]

I just did

[prisma mesa]

It still wont be perfect though

[prisma mesa]

because of this.

[shut rose]

No

that just means that the real isnt in the list yet

[prisma mesa]

I'll have to use hilberts hotel to destroy your argument then

[shut rose]

I used hilberts hotel to make the argument work

[prisma mesa]

and ill use it to show that your argument doesnt work lol

Okay, so you are saying that if you have hilbert's hotel with all rooms filled, then you can acommodate infinitely many guests by shifting the guests

So say that "Guest 1" lives in Room 1, Guest 2 lives in Room 2 etc...

now suppose that infinitely many new guests arrive, and form a queue

ill then call the first one in the queue "Guest -1" and send him to the first room, while sending guest 1 to 2nd room, guest 2 to 3rd room etc...

performing your shifting

then I'll call the 2nd one in the queue "Guest -2" and send him to the first room, again shifting all the guests

and then I'll do the same for all the remaining guests

my question now is, in what room will "Guest 1" end?

[shut rose]

somewhere

which is all that matters

[prisma mesa]

where?

I wanna know his room number

[shut rose]

cardinality of Z?

[prisma mesa]

that's his room number?

[shut rose]

actually + 1

but yeah

[prisma mesa]

yeah, that doesnt sound like a natural number to me...

and rooms in hilbert's hotel are only numbered with natural numbers

and that's where your argument crumbles down

you cant do this infinite shifting

because the guests won't end up occupying rooms numbered with finite numbers

they'll essentially end up outside of the hotel

without any room to live in...

[shut rose]

natural numbers are not finite though

[prisma mesa]

Yes, but every natural number is finite

51351353 is finite

6251349889135781357080135890 is finite too

but Guest 1 won't live in any finitely-numbered room

[shut rose]

well hold on

you could fit another N into N right?

[prisma mesa]

Yes, but not by this infinite-shifting

you would need to send guest in room n to room 2n

then all odd rooms will be empty

and you can fit the another N to them

the difference between these 2 ways of doing it is that in the second one, you can actually tell in which room will which guest end up.

In your shifting method, you can't tell that. And furthermore, you even know that e.g. guest 1 can't be in any room

[shut rose]

Ok so I can't say where Guest 1 is if I add infinitely many guests to the start, but I also can't say where the last guest is if I just take the normal hotel with no extra numbers

[prisma mesa]

yes, because there is no last guest

but you can tell where guest 531513513135 is

and where guest 15335Z13501359818390586138506890135689096853861906895 is

and where any guest is

[shut rose]

If there's no last guest then there's no last room

[prisma mesa]

every guest has a number, say N. And that guest lives in room N. So we can tell where each guest lives

[shut rose]

So I can always fit more people into it

[prisma mesa]

yes, there is no last room

[shut rose]

I won't ever run out of rooms

[prisma mesa]

Why?

[shut rose]

There's no last room

Or how about this

I move all initial guests to the even numbered rooms

And then I have infinitely many odd numbered rooms where I put the reals

[prisma mesa]

how do you put them there?

what guarantees that there will be no reals left in the end

[shut rose]

Because there is no end

[prisma mesa]

if there is no end, how can you end up accomodating all reals?

because there will be some reals left, at every point in time

[shut rose]

But there wont be because I have an infinite amount of ood numbered rooms

[prisma mesa]

Yeah, good for you.

But how are you gonna acommodate all reals?

how exactly? What will you tell them in order to make sure they all get to their rooms

[shut rose]

It's a free for all

All that matters is that there is a pair of a natural to a real

[prisma mesa]

Wdym?

oh, like you let them choose their rooms?

[shut rose]

yes

[prisma mesa]

lol, anyway, how do you guarantee that after everyone chooses their room, no 2 reals will have chosen the same room?

[shut rose]

they're polite

[prisma mesa]

the only way I can think of is by making them choose their rooms one by one. But that would require infinite amount of time...

[shut rose]

well real guest 1 will take 30 seconds to choose, guest 2 will take 15 seconds,...

[prisma mesa]

Who is guest 1?

there is a real number of them

[shut rose]

random

[hearty turret]

i think part of ur confusion comes from slightly fuzzy notions of what different sizes of infinities, functions etc are

[prisma mesa]

we got a hilbert hotel inside hilbert hotel now

[prisma mesa]

how do you guarantee that all guests will get their natural number?

[shut rose]

because there is an infinite amount of odd numbered rooms

[hearty turret]

this is an area of maths that you really need to properly like study rigorously to answer "why doesn't my fuzzy notion of infinities work"

[shut rose]

the reals are chosen randomly and then proceed to room 1, then another random real goes to room 3, ...

[prisma mesa]

i was talking about these natural numbers

how do you guarantee that all guests will end up having their N, so that they can pick in 60 * (1/2)^N seconds

and you got another hilbert's hotel... and we could repeat the same arguments we had before and get in the exact same situation

[shut rose]

I don't follow

Each real gets picked randomly and sent to room 2n + 1 where n is how many previous reals were randomly picked

[prisma mesa]

how do you guarantee that no 2 will pick the same room?

[shut rose]

Just said how

They get picked randomly and get sent to room 2n + 1 where n is how many previous reals were randomly picked

[prisma mesa]

oh, i see

this is an infinite process thoguh

there will be no point in time, where all guests will be accomodated

[shut rose]

there will

after 1 minute

[prisma mesa]

So you are using this

[shut rose]

yes

[prisma mesa]

but note that there is a real number of guests. There is guest pi, guest 5.531413, guest 0.12413515431.... etc

how can you be sure that you can assign every single one of them a natural number

so that you can do your guest-n thing

[shut rose]

you could use the same argument to say that all natural guests wont fit to a natural sized hotel, so its not valid

[hearty turret]

again you're doing an infinite process wrongly

[shut rose]

its a random pick

[prisma mesa]

Tell all the guests to move to room, which has their number. Done.

[hearty turret]

u'll have to do this infinitely often, and so in the end, u can't define f(2) etc.

[prisma mesa]

cool, but you cant be sure that every real will get a natural number in the end

[shut rose]

the random picker machine picks the pairings instantly

[prisma mesa]

how can we be sure such machine exists?

[shut rose]

it just does

isnt that what an axiom is?

[prisma mesa]

Yeah, it comes right after the axiom that says that there is a square with 10 sides, because it just exists

now seriously, you cant just assume stuff to exist

there are axioms which guarantee that some things exists

but afaik, there is no axiom that guarantees existence of your random picker machine

in fact, we can prove that such machine cant exist, by doing the diagonalization argument

[shut rose]

the diagonalization argument makes no sense

I can just add the new number to the hotel

[hearty turret]

how familiar are you with a proof by contradiction?

[prisma mesa]

Let's stop with the hotel now

Assume that there is a bijective function f: N -> [0, 1].
So e.g.
f(1) = 0.123456789...
f(2) = 0.234567890...
f(3) = 0.531411433151....
etc...

Now you can do the trick, and come up with a number in [0, 1] that isn't in the range of f, and hence f can't be bijective.

once more, this is the proof

What this proof shows is that given any matching, there is something missing

[prisma mesa]

So yes, you can add new number

but there will be something missing

and yes, you can add it

but there will be something missing

and yes, you can add it

but there will be something missing

...

and there is no proof method or axiom that allows you to do infinitely many steps at once

[hearty turret]

basically, this shows that no matter what clever thing u try to do to add to ur function, it will always be missing something

[shut rose]

Assume that there is a bijective function f: [0, 1] -> N.
So e.g.
f(0.123456789...) = 1
f(0.234567890...) = 2
f(0.531411433151....) = 3
etc...
now add + 1 to the last natural and boom new number and its missing

[prisma mesa]

last natural?

wdym?

is there last natural?

which one?

[shut rose]

the new real number also relies on there being a last digit

otherwise you will never have the number

there will always be one more digit to diagonalize

[prisma mesa]

it doesnt

[prisma mesa]

the real number is $\sum_{n=1}^{\infty}\frac{1}{10^{n}}\left(d_{f(n)}\left(n\right)+1\right)$

[thorny flame]

MæthIsAlwaysRight

[prisma mesa]

Where d_f(n) (n) is nth digit of f(n) and the addition is modulo 10

the difference between this and hilbert's hotel is that im only defining the real number, and I defined it. Yes, it is defined with use of infinitely many numbers f(n), but what? I know for sure that such real number exists, since all it's digits are valid and can even be computed. While in your hilbert's hotel argument, you were much less specific, you assumed that there is some machine, that can assign naturals to reals uniquely, or you just said that the real numbers will go to some rooms

and you didn't account for the possibility that it might be impossible

you actually assumed the conclusion while trying to prove it

[shut rose]

Ok... so instead of adding 2 to the "last natural", how about I sum all of them? Won't that create a new natural that's not in the list?

[prisma mesa]

That's assuming that sum of infinitely many naturals will be finite

which it won't

[prisma mesa]

this can actually shown to be finite by some simple analysis. It's smaller than sum of 9/10^n, which = 1 (since 0.999999999... = 1)

[prisma mesa]

1 + 1 + 1 + .... won't be natural for sure

nor will 1 + 2 + 3 + 4 + ....

nor will any other sum of infinitely many naturals

[shut rose]

Couldn't I apply the diagonalization to other places? Like what if I make the indexes real too? Then I get the new number which isn't in the list... so are reals bigger than reals?

[prisma mesa]

the problem will be proving that the new number isnt in the list

it might already be there

like

f(0.12124124124...) = 0.12124124124...
f(0.3141513535...) = 0.531341414...
f(0.36134...) = 0.941234153...
....

can you explain your argument on this example?

[shut rose]

Well I'll create a new number with the formula that you mentioned

[prisma mesa]

Ah

I see

[prisma mesa]

well, but this list is larger than naturals

as proved previously

but reals can only have |N| many digits

so doing diagonalization wont do anything, as the resulting real will only differ from |N| other reals

[prisma mesa]

In order to even perform diagonalization, you would need to have this list numbered:

1. f(0.12124124124...) = 0.12124124124...
2. f(0.3141513535...) = 0.531341414...
3. f(0.36134...) = 0.941234153...
   ...

but this numbering wont exist

since there are more reals than naturals

[shut rose]

.close

[topaz sinew]

Channel closed

Closed by @shut rose

Use .reopen if this was a mistake.

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[raw marten]

Does talking about adding a value to a set make sense in math?

[raw marten]

as in $S:=S\cup {value}$

[thorny flame]

>_<

[raw marten]

or should i not call it add a value to a set in my solution which someone has to read

[vernal shard]

What’s the context?

[odd pagoda]

well informally it would be fine to call it that I suppose. as long as you also write down that union

[raw marten]

we have a multiset S and remove two values a and b from it and add two values a+b and 2|a-b| to it

$S:= S-{a,b}+{a+b,2|a-b|}$

[thorny flame]

>_<

[topaz sinew]

@raw marten Has your question been resolved?

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[visual ravine]

can you resolve that?

[little lantern]

what are your thoughts?

can you say in words why there is a lowest number

like why not 0

[visual ravine]

it isnt the answer

i think the same

thought*

[dim matrix]

I can imagine that this is x + (x + 1) + … + (x + 9) = 230

[little lantern]

touche

[visual ravine]

but, what is the answer

[little lantern]

we're not supposed to give you the answer

[little lantern]

that sounds right to me

[visual ravine]

can you speak spanish?

[little lantern]

No :x siempre uso el traductor de Google.

[visual ravine]

I always speak spanish, but i can also speak english

[little lantern]

👍

i think fellow's solution is correct

[visual ravine]

its not 23

...

[visual ravine]

its not 23

[little lantern]

he didn't mean it was 23

he said to solve this

x

• x - 1
• x - 2
• x - 3
• x - 4
• x - 5
• x - 6
• x - 7
• x - 8
• x - 9
  = 230

for x

x is the number of cards of the winner

[visual ravine]

it isnt the answerrr

can you resolve that?

[little lantern]

i had no choice

[visual ravine]

I love you bro xDDD

thanks

[little lantern]

don't tell the mods about this

np lol

(that was a joke)

[topaz sinew]

@visual ravine Has your question been resolved?

Channel closed

Closed by @visual ravine

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[midnight saddle]

how do i solve tihsd

[midnight saddle]

i get this after

but im looking at the answer key and the answer key just turns the x^9 into -inf

how does that work

[rose sierra]

x^9 becomes -inf as x approaches -inf

[midnight saddle]

and so why does 10/x^5 become 0

because you're basically dividing by a number close to -inf>?

[neon iron]

ye

a

[midnight saddle]

ok thanks

'

and how do i start on this one

[neon iron]

also no

[fallow heart]

Factor out an x⁴ from the square root argument

And also factor out an x² in the denominator

[midnight saddle]

that gives me x^2 sqrt(1+8/x + 2/x^4)

i thinkj right

[fallow heart]

Then you can simplify the x² which will be on common

[midnight saddle]

then i have this right

[fallow heart]

Yep

[midnight saddle]

then the fractions all bcome 0

and then you get sqrt 1 which is 1

so 1/5 right

[fallow heart]

Actually it's -8 on the bottom but doesn't matter

[midnight saddle]

ya right

[fallow heart]

Awesome, well done 💪

[midnight saddle]

this one i factrored out the x squared in both the things

[fallow heart]

Unfortunately this technique doesn't work here, unless you know Taylor expansion

[midnight saddle]

sadly no

maybe i did learn this actually

im not sure

would i learn that in a cal 1 class?>

[fallow heart]

Here you have to rationalize, i.e. multiplying and dividing by √... + √...

[fallow heart]

I don't know, where I live in Italy classes are quite different

[midnight saddle]

wdym rationalize

divide by the square root?

[fallow heart]

This

[fallow heart]

Nope

[midnight saddle]

oh divide by the conjugate

[fallow heart]

https://youtu.be/eQaj3IOAVes?feature=shared

Like this

Multiplying and dividing by the conjugate

[midnight saddle]

multiplying on toip

and then dividing on the bottom

ya

[fallow heart]

Because otherwise you would change the function

[fallow heart]

No, you multiply both top and bottom

Or equivalently you multiply and divide the whole function

[midnight saddle]

but i have no multiplciation on the bottom

its just 1 x the conjugate

which is the conjugate

[fallow heart]

Yeah, that's still a multiplication

The number 1 is just not written, but it's there in the denominator

[midnight saddle]

okay then whats my next step

[fallow heart]

Doing calculations

[midnight saddle]

becomes a diff of squares no?

[fallow heart]

Exactly

[midnight saddle]

cancel the square root

[fallow heart]

Then you can factor out (carefully) an x² from the bottom

[midnight saddle]

gives me 12x

[fallow heart]

Yep

Btw now I'm going to bed
I'm sure there are other helpers available

[midnight saddle]

after i hvae this what should i doi

oh ok

thanks

[fallow heart]

You should do this now

And after that you simplify the x which will be in common between numerator and denominator

[midnight saddle]

But how would I do that from the numerator

Ohhh

But I can’t cancel the x^2 if it’s in a square root

[topaz sinew]

@midnight saddle Has your question been resolved?

[clear oasis]

you little black niggеrs nerds slaves!

[midnight saddle]

😭😭

[midnight saddle]

.close

[topaz sinew]

Channel closed

Closed by @midnight saddle

Use .reopen if this was a mistake.

[topaz sinew]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[upbeat minnow]

is the + 2 here just saying take integral from 3 to 7 of y=2 with respect to x and just add it to the other integral of f(x)

[woeful drift]

sure

[upbeat minnow]

ok cool ty

.close

[topaz sinew]

Channel closed

Closed by @upbeat minnow

Use .reopen if this was a mistake.