precalculus

[noble lava]

So pretty difficult

[hoary iris]

I see

[hoary iris]

yeaaaaaaaaaaaaaaaaaaaaaaahhhhhhhh

[noble lava]

I'd show you the solution except it would ruin the satisfaction of doing this yourself when you're done with limits and can execute things quickly

[hoary iris]

My question is nothing compared to this!💀

[noble lava]

Well you're just starting

[hoary iris]

Yeah!

[noble lava]

Also your question was 1^inf form and you said you learnt only 0/0

[hoary iris]

Yes in my JEE class

I have learnt that in my normal 11th

[noble lava]

Oh hsc?

[hoary iris]

yeah

[noble lava]

Same

My instructor was hella surprised when i started spitting lhospital to derive standard limits

Bro was like stop, lhospitals is a weakness

[hoary iris]

[noble lava]

And until recently i didnt understand how true that was

[hoary iris]

really? just recently?

[noble lava]

But now im stuck in my stubborn habits and i cant change how i do things

[hoary iris]

[hoary iris]

but you do know other approach right?

[noble lava]

Yes i spammed lhospitals for mains but when i started doing adv prep a few months after completion of my course i got so many roadblocks

[noble lava]

Duh lol

I just told you two

[hoary iris]

two is plenty to this

[noble lava]

Ik theres some stuff like taylors as well but idk shit abt that

Will learn in college prolly

[hoary iris]

[noble lava]

Also keep in mind that series expansion is a very powerful weapon

Just learn it for sin cos and ln and you're set

[hoary iris]

yeah I haven't tried to use that rest of my life till now

[noble lava]

Another thing i ignored applying due to lopital spam

But now ik its easier and i do it occasionally

Not really been solving limits much tho recently, mostly indef integ

[hoary iris]

spamming l hop?

[noble lava]

The real question is why am i doing math daily in my vacation

[hoary iris]

doing math in vacation lol?

[noble lava]

Like ngl ive been in this server four days and

[hoary iris]

It may please minds of mathematicians lol

[noble lava]

Thats 500 messages per day

More math than i did in the week before mains

[hoary iris]

💀

[willow bear]

i have 768k messages and have been in this server for 8.5 years, calculate my rate of messages per day.

[noble lava]

Tho tbf most of it is easier since i usually only pick those i can answer acchese so i can help the asker

[willow bear]

if you need an exact start date: january 15, 2017

[hoary iris]

[noble lava]

,w 76810^3/(8.5360)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by executor.1011

[vagrant nymph]

247

[noble lava]

I aint doing that shi bruv

[willow bear]

please don't call me "brother" or any variation thereof.

[noble lava]

Im not calling you brother

Its like

"Bruh", the expression

[willow bear]

you called me "bruv" just now and i told you not to do that.

[noble lava]

Ok soz soz

[noble lava]

How long you been here though?

[modest bolt]

march 18 2024, now calculate

[noble lava]

For her messages or yours?

[modest bolt]

monkey d luffy joined at that day

[noble lava]

O i didnt see what u replied to lol

,w 4404/446

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by executor.1011

[noble lava]

,w 2202/23 in decimals

Ooh

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by executor.1011

[noble lava]

Lmao period 22

That's a hell of a thing to do by hand

[noble lava]

I'm assuming you expected me to do the division right

[hoary iris]

since 2022

in this server

[noble lava]

What why did he say 2024 then lol

[hoary iris]

about 3 years

idk

lol

[hoary iris]

How bruh!?

eventhough only 4000 msgs lol

but you lol executor

[noble lava]

Fr

[hoary iris]

yes(I ain't an active boi anyways)

I will come sometimes to help

sometimes to get help

[noble lava]

Well i have nothing to do rn except do coding math and games

[hoary iris]

sometime to chill

[noble lava]

So im here a lot

Vacations are pog

[hoary iris]

When are you going to get busy again? lol

[noble lava]

In a month

College begins

[hoary iris]

anyways enjoy your vacation prolly

[noble lava]

But its fine ive been on holiday for 20 days already

[noble lava]

Tyty

[hoary iris]

and watch one piece in this month

lol

[noble lava]

Why does everybody tell me to watch one piece its a thousand episodes

The longest anime ive watched is naruto

[hoary iris]

everybody? lol

You won't regret watching it

[noble lava]

Ive watched like 50+ anime till now nothing is close to 1000 episodes

[noble lava]

Ok i might try

Rn I'm watching peaky blinders tho

[hoary iris]

I have watched a single anime with a range of 1132 ep

[noble lava]

Thomas shelby

[noble lava]

I'm assuming that's one piece? Or something else??

[hoary iris]

not only that though

[hoary iris]

yea

[noble lava]

What's the next longest

After op

[hoary iris]

aot?

or ds

[noble lava]

You've watched?

[hoary iris]

yea

[noble lava]

O

One anime i hate is mha

[noble lava]

O means oh

[hoary iris]

[hoary iris]

lol

[hoary iris]

literally me

[noble lava]

I started watching it

Disappointment in 2 episodes

[hoary iris]

I haven't touched it

[noble lava]

Just what is that shit

[noble lava]

I instantly left

[hoary iris]

you won't regret even a single ep in op i tell

you will die in oda's foreshadowing lol

lol

[noble lava]

Alr cool

[noble lava]

Allen app??

[hoary iris]

yeah howdya know?

[noble lava]

Me allen too lol

This wasnt so developed in my education period tho we just did things on whatsapp and offline

Good to know theyve integrated some stuff

[hoary iris]

I am allen online

btw

[noble lava]

O makes sense

How is online?

[hoary iris]

good for my tight schedule of school

but too hard

[noble lava]

Oh you go to a real school?

[hoary iris]

to keep up

[hoary iris]

are you integrated school?

[noble lava]

Dw it's the same for offline people

[noble lava]

Yeah

[hoary iris]

I see it's good for that

but I am in a real problem

lol

[noble lava]

Hard to do real school exam though

But i concentrated so it was easy

Got 197/200 in cs so that just clutched big time

[hoary iris]

[noble lava]

Till what time real school

[hoary iris]

3 for now as it is started just now and original till 6

[noble lava]

Oh long time

Allen lectures when

[hoary iris]

from 6

[hoary iris]

what is this btw?

[noble lava]

O so school close to home

[noble lava]

Hsc score

Bifocal cs

[hoary iris]

[noble lava]

Never sacrifice sleep tho btw

[hoary iris]

takes 6.15 to reach

[noble lava]

Do you?

[hoary iris]

thank you

sleeping at 12

normally

[noble lava]

Nice

Ive seen lot of jee ppl do it

Long term mein pachtayenge

[hoary iris]

sorry(idk hindi)

[noble lava]

I tried for 2 weeks during jee

[noble lava]

Oh

Pachtayenge= will regret

[hoary iris]

oh i see

[noble lava]

You're nri?

[hoary iris]

you did? lol

[noble lava]

Did not work

[hoary iris]

non-residental indian??

[noble lava]

Or might just be from south or north lol

[hoary iris]

south lol

[noble lava]

Yeah

[hoary iris]

I see

[noble lava]

I speak kannada

[hoary iris]

ohh good i speak tamil lol

[noble lava]

Ooh my future college might be in chennai

Still thinking tho not decided

[hoary iris]

lol

[noble lava]

Also were talking in precalc

Lets go disc 2

[hoary iris]

yeah we may die here

[noble lava]

Just realised

[hoary iris]

ping me

[modest bolt]

when you check someone's profile, it tells when they joined the server below 'about me' part

and i will you if you talk here now, if you wanna say something to me, ping me in #chill

[burnt cape]

Hey @wraith escarp sorry to bother you, but is this a corner?

[wraith escarp]

yes

there are two different slopes at that point, aka the derivative is discontinuous

[burnt cape]

gotcha, so with my corners being here:

Where/what exactly is my slope? or point i place for f'()

[wraith escarp]

there is a jump in f'(x)

itll be f'(x) = 0 until -1, then start being f(-x) = -1 after that

[burnt cape]

im confused on how to graph that on f'

[burnt cape]

Like this?

[wraith escarp]

a) the slope isnt -2 for the downward part of the graph
b) there should be another jump at x = 3 since f(x) starts going up

[burnt cape]

?

[wraith escarp]

not correct past x = 3

[burnt cape]

so at 4?

[wraith escarp]

whats the slope at x = 4 and whats it at x = 5?

does it change?

if not, why does your f'(x) change

also, speaking of which, what is the slope of f(x) at x = 4?

[burnt cape]

i doesnt change and the slope at x= 4 is 1

[wraith escarp]

then why is f'(4) = 0

[wraith escarp]

you are making random lines

the slope at x=4 is 1 as you mentioned

therefore f'(4) should be 1

[burnt cape]

is it not 1 though since it passes through (4,4)

which slope is 1

[wraith escarp]

you arent trying to make the slope of f'(x) match the slope of f(x)

the actual y value of f'(x) is the slope

f'(x) should contain (4, 1) because the slope of f(4) is 1

it should also contain (5, 1) for the same reasons

[wraith escarp]

whats the slope at x = 3.5

[burnt cape]

nothing so i have to make it go to the 3

[wraith escarp]

what do you mean nothing?

[burnt cape]

well theres no line there i jumps from 3 to 4 so shouldnt it be

[wraith escarp]

yeah this one is right

the slope at x = 3.5 is also 1

and your new correct answer does in fact have (3.5, 1) so its looking good

[burnt cape]

so can you walk me through the steps again

[wraith escarp]

i mean your answer is right, do you have questions about specific parts of it?

ie why some things are how they are or how we got something specific?

[burnt cape]

im just confused why we used straight lines for everything even though after the dashes it goes up

[wraith escarp]

well

"it goes up" is the misunderstanding

the function does go up, but the slope doesn't

x = 0, 1, 2 all have the same slope

it doesnt "go down"

[high steeple]

any tips on memorizing very long formulas for someone with weak memory? 🥀

[river drift]

you shouldn't be in a situation where you need to memorize very long formulas

[high steeple]

what about college entrance exams

[echo sinew]

Which one for example?

[willow bear]

yeah can you show the long formulas you're finding yourself having to memorize

[high steeple]

ive never taken an entrance exam so idk what to expect

example here

[high steeple]

here

[high steeple]

.

[willow bear]

hm

well, this formula's written in a rather unwieldy way, but if you aren't familiar with sigma-notation it might be a bit unavoidable.

though again i would advise AGAINST memorizing it into a thousand fragile pieces

and instead learning about binomial expansions in depth

[opal sable]

just learn how the formula is derived, and then you will learn the formula, because, you know how it was created, and how it works. You shouldn't just mug up. Anyways it is your choice

[arctic dagger]

it's also not very hard to memorize

like you should see the pattern in binomial expansion formula

[opal sable]

yeah.

but what about other formulas

but anyways, how its derived is the main part

[willow bear]

i think that the longest formula worth "memorizing" is the law of cosines

[arctic dagger]

true

for me personally it's worth deriving

I'm still on my quest to get used to it by deriving

[willow bear]

i didn't say you should memorize it blind

its derivation is pretty important to know

but at the same time, when you're practicing with it, thinking about the derivation every single time gets taxing

[hushed sphinx]

I'll raise you the quadratic formula.

[willow bear]

about the same length innit

$c^2 = a^2 + b^2 - 2ab \cos(C)$

or maybe

$\cos(C) = \frac{a^2+b^2-c^2}{2ab}$

vs.

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

[obsidian monolith]

Ann

[hushed sphinx]

Hmmm, the quadratic formula feels more involved to me ... but I acknowledge that is not an exact science.

(Ironically, I can remember the quadratic formula, but I need to look up the law of cosines).

[ionic ether]

I think it is much easier to remember the law of cosines in the 1st form as it can be easily seen that Pythagoras theorem is just a special case of law of cosines.

[willow bear]

yeah i was just giving both forms to make a comparison on complexity/perceived "length"

[hidden sun]

what about cos(x+y)?

[willow bear]

oh yeah hm

that's longer innit

[hushed sphinx]

Is that worth memorizing, though?

[willow bear]

yes imo it is

[hidden sun]

Yeah

Every formula is worth memorizing if it saves your time

[hushed sphinx]

Hmm, at least I've never bothered. If I need it, I'll either look it up, or derive it from e^it.

[hidden sun]

Only do it if you know how to get them at any moment

[willow bear]

if you're a school kid who has not yet learned about C then it's a bit of a no go

[hidden sun]

(we don`t talk about fermats last theorem)

[willow skiff]

pq-formel, next

<@&268886789983436800> spa

spam

Moderators Need A Spa Day

[hushed sphinx]

What is that?

[willow skiff]

oh I keep forgetting you're not German

here ya go

ya filthy American

if you have x^2 + px + q, so you just need to divide b and c by a

[hushed sphinx]

I'm not American either.

[willow skiff]

ah

[hoary iris]

lol

[vagrant nymph]

Is my solution correct?

It feels wrong

But the ans is correct

[void charm]

what do quadratic function do with geometry formula?

behold the final boss of basic geometry, superior Menelaus's formula

I mean basically this is harder to memorise than any formula

[modest bolt]

BP × AM/MB = AN/NC × PC
idk why I feel this is easier to remember

[willow skiff]

oh that reveals a possible proof right

triangles APN and NPC are related by scaling

and so are triangles AMP and BMP

[modest bolt]

ngl Idk how does that reveal any proof but I really meant I only feel like writing the same equation like that is easier to memorize, not like I know how to prove the equation

[storm lodge]

no

its quite easy to memorize if you solve problems with it

[sly cipher]

just use Thales omg

[willow skiff]

how is Thales related?

[modest bolt]

if you take P at infinity, it becomes thales theorem

[willow skiff]

oop- ah

the name is so shit, cause it could also refer to right angle inside a circle

[vagrant nymph]

anyone?

[hollow fractal]

I would love to help but i can't read english handwritings.
From what i can read you calculated: (1+m/8x)^(1/3) = (1+m/24) ?
Correct me if i'm wrong or they're symbols i don't know about

[hoary iris]

,, \sum(ab)=\sum(a)\sum(b)?

[obsidian monolith]

Monkey•D•Luffy

[vagrant nymph]

Yes

Binomial approximationn

[willow bear]

not in the slightest

does not even work for sums 2 terms long 💀

[drifting oyster]

$\sum(ab)=\int a(x) dx*\int b(x)dx$

Trust me bro

[obsidian monolith]

Enterlessguy

[hoary iris]

But thank you for this bro

[hoary iris]

How to use this bro?

convert a and b into x?

[drifting oyster]

well I was assuming you were using sequences for a and b

So just let the sequences be defined for R instead of N

Trust trust

[willow bear]

for the record, i will be a killjoy on purpose and say that @drifting oyster's thing is completely false and also nonsensical.

[hoary iris]

Thank you, ann. I literally thought that is true lmao

[willow bear]

ok yeah this sort of naïveté is exactly why a space like this needs to be free of falsehoods stated so brazenly as @drifting oyster did

[hoary iris]

I thought it is true since sum and integral has some relations to each other

I thought It is super helpful

but so sadly it is not true

for my unfortune

lmao

Also @modest bolt Do you know the relation b\w sum and int?

Are you writing the relation????

If yes, nvm me lmao

Hell you really did write the relation

[modest bolt]

int is just infinite summation of smaall x but you can know better by google

[noble lava]

You should understand reln betn integral and sum by looking at the example of an area under the curve problem

[modest bolt]

i am talking about basic definition of integral which we learn to find area under curve, idk any other relation if there is

[noble lava]

You make infinite small rectangles and add all their areas together to get the area of the curve, which is the integral of the curve

[modest bolt]

there are good animation vedios to explain that, you can watch if you want

[noble lava]

Yeah

[gray magnet]

i know there is a formula for this

why does this not work

it works for one but there is another

[raw hill]

What if the difference is 7pi/12 instead

[gray magnet]

my number is right but their is another soultion

[raw hill]

Does what I said not apply?

[gray magnet]

wouldn't it get picked up by the mod

[raw hill]

What

That tells you if this angle is 5pi/12 (absolute difference between the two angles with the x axis is the indicated angle by exterior angle theorem)

But my point is that this angle could also be 7pi/12

Because then the acute angle would be pi-7pi/12=5pi/12

@gray magnet Hello?

[gray magnet]

yeah your right

i forgot that arctan only gooes anticlockwise

i though it would account for this

[final ore]

i know its not in english

but why is that the k is going to n-1?

shouldn't it be both k=0 to n?

[abstract musk]

can someone please explain why the null set is a subset of all the other non-empty sets...I mean the null set doesn't contain any element of another Set.

[distant ivy]

I think its so that you dont get a second a_n*b_n term that you already got from the first term

[final ore]

ahhh

[cinder wyvern]

hey

im learing deriviatives rn

i like calculus its very fun

what can i expetc next

[silent vine]

academic suffer and Frustration

[cinder wyvern]

nice!

[rough arrow]

tfw you realize 1/x looks the exact same as 1/y

[rough arrow]

more derivatives, and antiderivatives, and going back to limits again, and then back to derivatives, oh and you remember that math trick you forgot from middle school? yeah you're gonna use that again, but only for a week.

✨ m. a. t. h. ✨

[solar dagger]

can anyone tell me the definitions of tangent lines, cause it seems like its really useless and rendundant to me

from what i know Tangent line is a point in a curve that sort of like kisses the point that from the lines itself it goes forever, but then Why do we need all of this fancy Formula and others just to decide that one point

and what is actually the use case of this tangent line?

[soft plover]

it is a line that touches a curve at exactly one point

it is used to calculate the slope of a curve at a certain point

[solar dagger]

the slope?

isnt tangent line return a line equations

rather then a slope

cuz if u want a slope u can just use the point slope formula for it

[whole void]

wdym “that math trick u forgot from middle school”

[whole void]

Nope

[whole void]

I don’t know if this is an accepted definition, I haven’t seen it before, but it’s something I thought of. A line say l(x) is tangent to a curve say f(x) at a point say x = a if l(a) = f(a) and there exists an open interval I containing a such that l(x) >= f(x) for all x in I or l(x) <= f(x) for all x in I

if this is wrong, please let me know but I think this works?

I think there are subtle differences with this and the calculus definition I believe

what do u think? @solar dagger

[solar dagger]

hmm so in short it is like uhm a line that Goes to the point x =/> or basically shows the direction

but while solving the tangent line problem itself we can know the Slope of it as we most of the time

will need to find the slope first

[whole void]

idk what u mean?

[solar dagger]

like line a goes to line x?

[whole void]

there’s no line a and line x idk what u mean

[solar dagger]

then wdym?

[whole void]

No I don’t know what u mean

[soft plover]

why

[solar dagger]

idk what this mean either lel

if im wrong and u dont know what i mean then i dont know what that mean either.

[whole void]

A tangent line can intersect a curve again, further away

[whole void]

I think what I said is (hopefully) very clear. which part don’t u get though?

[solar dagger]

all of it honestly.

[soft plover]

oh right

[whole void]

then take more time to think about it

[solar dagger]

but i think i already got the definitions of tangent line it self, just finished doing some research

[whole void]

what is it then

[solar dagger]

its basically a Direction from point a to be point b

[willow skiff]

it's the unique line that passes through (a, f(a)) and where the slope at x = a is f'(a)

given a function f and a particular x-value x = a

[solar dagger]

what is (a, f(a)?

[willow skiff]

it's a point's coordinates

[whole void]

is what I said fine btw? Is there a reason what I said isn’t used more often? I feel like it’s simpler at least to understand intuitively

[willow skiff]

yeah that's a plausible real analysis definition but their ability isn't there yet

[solar dagger]

it should be fine, its just harder to understand smt like that, i cant understand it at all though.

[willow skiff]

when you start using open intervals you'll have lost them already

[solar dagger]

oh u can use function for a point coordinate?

[willow skiff]

yeah!

x-coordinate = a
y-coordinate = f(a)

[whole void]

I haven’t done real analysis

[solar dagger]

woah i just knew that

but why u use function?

is there any special reason on that?

[willow skiff]

it's better to think of a line in terms of a point (the 0th derivative) and the first derivative

[solar dagger]

also tangent line always return a line equations right not a slope? correct me if im wrong.

[willow skiff]

this definition is perfectly fine locally

it's just not phrased in the language of calculus

that's moreso a geometry definition

[whole void]

wait it’s not though

[solar dagger]

uhm what is 0th derivative and first derivative? do u mean the point?

[willow skiff]

yeah, a tangent line is a line

[willow skiff]

oh yeah you don't know about Taylor series

[solar dagger]

i see oke oke.

[solar dagger]

yeah not yet

[willow skiff]

Taylor series talk about the best polynomial approximations to a function centered at a given point

a lot of functions like sine and cosine, or e^x aren't polynomials

[solar dagger]

function centered?

what is that?

[willow skiff]

the function exactly matches at that particular point

[solar dagger]

also if u dont mind can u tell me the basic about taylor series, i heard it was very beautiful and fun

[willow skiff]

as you move away, to the left and to the right, the approximation gets less accurate

[solar dagger]

havent learn about it at all though

[solar dagger]

so like 0,0?

[willow skiff]

https://www.youtube.com/watch?v=3d6DsjIBzJ4

[willow skiff]

yeah! that's a common Taylor series

we approximate the function at x = 0

[solar dagger]

😮

[willow skiff]

we don't necessarily have y = 0

y-coord could be anything

[solar dagger]

alright alright lets talk about the taylor later

[solar dagger]

will watch it soon

also back to the Tangent line

[willow skiff]

ok

[solar dagger]

usually the formula for tangent line is what? i asked ai and it says it was the point slope formula

im not sure if that is right though

lets say a circle

[willow skiff]

yes that's correct

[solar dagger]

i want to find a tangent line of a circle, did the formula will be different for like a Box/triangle.

[willow skiff]

yes

[solar dagger]

Oh?

[whole void]

I know what’s it’s trying to say, but the locally part makes it weird. Like how are these two different

[solar dagger]

do u mind tell me about the formula?

[willow skiff]

a local approximation follows epsilon-delta, so it must have the same slope at the point of tangency

[solar dagger]

waat there is two thing? the thing that crosses and touches?

i thought its only touch

[willow skiff]

yeah, so the left image is tangent at one point

it is a tangent line where it says 'touches here'

[willow skiff]

what do you want to know

[whole void]

south what’s that pfp btw

[solar dagger]

woah oke uhm this going to be pretty long conversation, cuz i always ask things too much most of the time.

soo like lets say i want to find a Circle tangent line, how can i do that?

[willow skiff]

the tricky bit is finding the slope at any point on the circle

https://www.youtube.com/watch?v=biGUxpfp3sw

watch this it'll teach you how

[whole void]

a circle is very nice actually

if u remember geometry

[willow skiff]

yeah that's another approach, by similar triangles

[solar dagger]

what kind of geometry?

[solar dagger]

kk will watch it

rn

[solar dagger]

i remember circle formula like pi and sort

[whole void]

The line from the center to the point of tangency is perpendicular to the line tangent to the circle at a particular point

[whole void]

@willow skiff

[solar dagger]

u referring to the standard form or general?

like the

[whole void]

It doesn’t matter

[solar dagger]

(x + h)^2 + (y + k)^2 = r^2

if im not wrong

u talking about this?

[willow skiff]

it's a local landmark of the jetty here

[willow skiff]

yeah

[solar dagger]

ohh then yes i do know, i actually just learned it yesterday

gtg now, need to wathc the video rq

then ill get back to here

[willow skiff]

but this approach just uses geometry

you don't need any equations to realise that

[willow skiff]

you can show it using calculus, so calculus always works no matter the shape

but then that's a bit overkill if you only want to know for circles

[whole void]

where’s here

[willow skiff]

Aus

[whole void]

eg the slope of the radius is 5/3 so the slope of the tangent line is -3/5

[whole void]

Oh cool

[solar dagger]

@willow skiff

just finished watched it, btw what is the different between Calculus method and geometric method on finding the tangent lines of a circle?

did calculus more accurate or what is the different?

[willow skiff]

the difference is in how you find the slope, so finding f'(a)

[solar dagger]

but the result will stays the same?

[willow skiff]

once you find f'(a) you can just sub into $y - f(a) = f'(a) (x - a)$

[obsidian monolith]

south

[willow skiff]

yes

[solar dagger]

i see yeah i think ill stick with geometric for now, until i understand calculus more

also what about if like a Box?

[willow skiff]

yeah i didn't realise you just wanted the circle

[solar dagger]

no no i mean

a curve

how can i find the tangent line for a curve?

[willow skiff]

I don't get what you mean by a box

[solar dagger]

a curve mb, like an oscilating curve

up and down

or quadratic curve

or cubic curve

[willow skiff]

okay for all those ones you need calculus

[solar dagger]

oh why is that?

[willow skiff]

calculus is the most general method

[rough arrow]

all of them

[willow skiff]

it's based on finding the slope of the line as you bring two points closer and closer together

when those two points are the exact same, that limiting slope gives you the slope of any curve

[rough arrow]

it seems hella pointless at first, but it'll keep coming back up over and over again throughout calc.

[solar dagger]

ohhh i see

[rough arrow]

and it'll be easier each time

[solar dagger]

yeah sure ill learn it

[willow skiff]

for circles we use the fact that the tangent and radius angle is 90 degrees

that's only for circles

[solar dagger]

yeah it is indeed kinda pointless until i realize the use-case in calculus

[willow skiff]

there's a few other classes of functions where you don't need calculus, excluding lines

[solar dagger]

then i need to learn about derivative first am i right?

or wrong

[willow skiff]

but then you'd have to be smart to think of how you could do it without calculus

[willow skiff]

start with limits

[solar dagger]

Oh oke wait wait

let me think rq lol

[rough arrow]

and this is really all it is. it's simpler than it seems at first... it really is just a line that uniquely touches this particular spot. this whole thing will make more sense when you get into derivatives and the like.

[willow skiff]

yeah it's a natural extension of point slope form

you literally replace m with the derivative at x = a

that's it

[rough arrow]

oh lol i'm hella behind

on the chat

[solar dagger]

uhmmm, what is this mean if u mind to elaborate it?

[solar dagger]

ohh

ohhh

[willow skiff]

only true for a circle

[solar dagger]

so its perpendicular

woooooooahhh but i still got question about circle since u talking about circle

[rough arrow]

circles are triangles and triangles are harmonic swings and harmonic swings are vibrations and everything is everything

QED ⬛

[solar dagger]

in circle geometric formula there is an extra (x - h) and (y-k)

and why is that? i mean the rest its similar to the standard form of Circle just with extra (x - h) and (y - k) also when i calc it, it seems like used for multiplication kind of thing but i believe there is a deeper Meaning in it.

[solar dagger]

yeah circle and triangles is soo related idk why.

[rough arrow]

hehehehehehehehehe

[solar dagger]

like the unit circle uses triangles for the circle

[rough arrow]

reasons. lol, the short version is "because, universe"

[solar dagger]

lol i mean that is true but

[rough arrow]

whatcha mean "extra"?

[solar dagger]

maths guy always ask for a reason and prove.

[rough arrow]

Are you talking about the -h and the -k?

[solar dagger]

(x₁ - h)(x - h) + (y₁ - k)(y - k) = r² this is Geometric formula to find the tangent line of circle

(x - h)² + (y - k)² = r²

and this is for the circle standard form itself

it looks pretty similar except for the

extra (x-h) and (y-k)

[rough arrow]

they're the same, though.

no, they're the same. 🙂 look closer.

[solar dagger]

yeah but they produce a different

equations

and result

[rough arrow]

the difference is....
one has an x and an x_1 <--- one is symbolic, one is defined
the other has two x <--- both are symbolic

[solar dagger]

yes i know that but

[rough arrow]

it's the same formula, but you're picking points for the tangent line, so you take up two of the coordinates

[solar dagger]

they two is different

try to plug some random coordinate of a circle

[rough arrow]

lol, I should be more careful with my words.

[solar dagger]

hmmm

[willow skiff]

it's to do with function transformations

[solar dagger]

i think this is right

[willow skiff]

$x \mapsto x - h$ moves the function $h$ units to the right

[rough arrow]

They're the same, as in, the tangent line equation is derived from the original equation

[obsidian monolith]

south

[solar dagger]

ait wait

dont use that kind of explanation i beg u

i wouldnt understand it at all lol.

[willow skiff]

then you need to go back and revise

[rough arrow]

It's not "extra"... (x-h)(x-h) = (x-h)^2

but in one, we "define" the x

and the y

[solar dagger]

revise what thing?

[willow skiff]

function transformations

here I'll link a vido

[solar dagger]

havent learn that at all ngl.

[solar dagger]

i think i get u

let me think rq

[willow skiff]

https://www.youtube.com/watch?v=MkP1LJR2PyM

[solar dagger]

ohh that is right @rough arrow

[rough arrow]

such as, if a known point on the circle is (5,2) then x1=5 and y1=2
so
(5-h)(x-h)+(2-k)(y-k)=r^2

[willow skiff]

you have gaps in your knowledge, cause you're self-studying or something right

you can't start calculus without having a deep understanding of functions

[solar dagger]

the x_1 and y_1 is uses for the tangent coordinate

[solar dagger]

ohh this, i have learned it before

[solar dagger]

yes im self-studying.

[willow skiff]

here's another example of what I mean

[willow skiff]

do you have a textbook you're following?

[rough arrow]

yep yep yep!

another fun one to realize... point-slope form? y-y1=m(x-x1)... that's 100% equivalent to y=mx+b, just written out so we can recognize exact points in the formula, which is therefore easier to create tangent lines

[solar dagger]

just youtube i dont have that kind of textbook unfortuntately

[rough arrow]

Check out something like OpenStax for a free textbook!

My school uses this book for our course 🙂 and it has practice software in it, too!

[willow skiff]

https://irp-cdn.multiscreensite.com/721e955d/files/uploaded/ebooksclub.org__Precalculus__Enhanced_WebAssign_Edition__with_Mathematics_and_Science_Printed_Access_Card_and_Start_Smart_.pdf

[solar dagger]

yeah so now i just need to know the reason behind it, by learning function transformation.

[willow skiff]

James Stewart's Precalculus for example

[rough arrow]

Desmos has free(?) lessons and calculator toys too

[solar dagger]

oh wow

[willow skiff]

yeah even if you follow Khan Academy you won't be that far off

at least it's organised and there's quizzes on every subtopic

[rough arrow]

and you get energy and plants and superpowers and stuff, lol

[willow skiff]

YouTube is good but it's not a replacement for an actual curriculum

[solar dagger]

honestly my learning pattern is not organizied at all

[rough arrow]

I love Khan but I don't use it consistently enough hahaha

[willow skiff]

I do think you shouldn't stress about if you're "ahead" or "behind" or not

[solar dagger]

i often jump from another to another and yet i still understand it. but at a different concept like this im loss

[willow skiff]

but if you try structuring your learning you'll find maths becomes easier

[solar dagger]

it might sounds abit funny that i know trig but not function transformation fully

so yeah i guess ill try

[willow skiff]

you know a sin(b(x - c)) + d?

[solar dagger]

do u have any tips on this?

[solar dagger]

yeah

[willow skiff]

you know what the a, b, c, d do?

[solar dagger]

the inside bracket shift or make it strecht

and the outside is

[willow skiff]

literally just work through one chapter of this book

[solar dagger]

for vertical shift

[willow skiff]

see how you go

[willow skiff]

great, so you do know

[solar dagger]

this is for precalc right?

[willow skiff]

but you haven't realised that it's the same for all functions

[willow skiff]

yep

[solar dagger]

yes Lol, math is actually really fun and myterious for me.

[solar dagger]

aight

[willow skiff]

most importantly practice the exercises

answers are online somewhere

[solar dagger]

wow the website is actually full of e-book about math thanks @rough arrow

[solar dagger]

alright last thing before i go and read some books, for a structured learning do u suggest me to Read a single book at the time until i finished it

or something else?

[rough arrow]

the reason is because of math, lol. i apologize if my descriptions are hella basic right now... i'm super tired, but here's why:
if we know a number is, say, 5, but we want to find a spot where it equals 3... we do math.

• 5-3=2, hey dope, we found a 3 in there!
  but what if we're dealing with x & y at the same time?
  well, same thing applies. use point-slope form. (I can't think of a good example right now... too sleepy, but I hope this shows how it's more simple than it seems)

lol i keep falling behind in the convo lollllllllllllllll

[willow skiff]

probably just work one chapter at a time

you can browse multiple books to see which one explains the best as well

main thing is just read and practice

if anything is unclear watch YT

but try to follow the book if you can

[rough arrow]

I'll add that I'm taking Calc 2 this summer, and the nice thing about Algebra, Pre-Calc/Trig, Calc 1, 2, 3... they all just build off each other.

[solar dagger]

yeah math is got alot alot of abstraction someetimes its just like really intresting and annoying to find the reason on why this happend or this happend because usually at school we only teached to remember something and the teacher doesnt even tell us the reason behind it, also you are right in every math formula there is alot lot lot of possiblity going on like a number 5 and 3 can become a coordinate or it can become this and bla bla bla.

[rough arrow]

sometimes linearly... one chapter builds to the next chapter

[willow skiff]

yeah literally don't look at anything before precalc

[solar dagger]

Alright sounds good

thanks man!

[willow skiff]

there's a lot of repetition

you don't need to look at alg 1 or alg 2 if you learn precalc properly

[solar dagger]

btw precalc is just about the basic of calculus right?

[willow skiff]

it's "essential maths before starting calculus"

[rough arrow]

other times in spirals... you'll learn a trick, put it on your reference card, then not use it for a while until you remember it exists when you're stumped 3 chapters from now

[solar dagger]

got it!

[rough arrow]

hence my joke earlier about "remember that math trick you learned in middle school?"

because really, math curriculum really just goes in spirals, endlessly 😆

[willow skiff]

if you're self-studying you don't follow what your school or your teacher is doing, by definition

you can go at your own pace

also a lot of schools have mandatory hours for learning mathematics and teachers need to find a way to fill up the time somehow

[willow skiff]

exactly

[rough arrow]

"hey, i know you're in the middle of some complex integration, but did you forget how fractions work?" <-- happens more often than you'd think, hahahahaha

[willow skiff]

about the spiral anology, which is very very useful and it's true

[solar dagger]

alright i gtg now guys, really glad that i meet you two, i learned alot today about how to learn and this tangent line.

thank you : )

[willow skiff]

after you learn precalc then you'll find that calculus uses precalc a lot, obviously

so you can revise precalc and learn calc at the same time

main thing is try to learn it well right now

90% of all calculus mistakes are caused by not understanding precalc

[rough arrow]

some of the precalc lessons are secretly teaching you calc... then you get to calc and learn it for real and go "hey waitaminute, this looks familiar!!!"

[steady peak]

Yello have a quick question, hopefully not interrupting anything
If I took precal dual this year, could I js take the precal AP test next year w/o taking the class

I feel like the class would lwk be the same, I only would have to study the frqs?

[willow skiff]

yes, that's correct

[rough arrow]

oh lol yeah, that's how AP stuff works.

[steady peak]

Nice thx

How do you even do math frqs tho

[rough arrow]

when you take the test, don't be me and forget to write down the time

[steady peak]

I'm also take AP calc ab this coming school year

[willow skiff]

there's not really a 'how'

[rough arrow]

lol, i showed up to math period and was like "where is everyone?"... teacher said "lol, the test was like 5 hours ago man, you missed it"

[willow skiff]

I will say practice with the formula booklet and underline the key bits of the question

[hoary iris]

Why $\sum_{k=1}^{\infty}\frac{1}{k^2}$ converges to 2 while $\sum_{k=1}^{\infty}\frac 1k$ diverges?

[obsidian monolith]

Monkey•D•Luffy

[uncut mulch]

to 2? do you mean pi^2/6?

series for 1/k can be shown to diverge from integral test

[hoary iris]

oh my bad

I thought it is 2

,, \sum_{k=1}^{\infty}\left(\frac{1}{2^k}\right)

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

this @uncut mulch

[uncut mulch]

that will be 2, yes

[hoary iris]

Is there integral approach to this?

[uncut mulch]

basic integral approach allows you to show that the sum is less than 2

getting the value of pi^2/6 is more complex,
(Basel problem)

[hoary iris]

I see

also this is more interesting that $\lim_{n \to \infty}\sum_{k=1}^{\infty}\frac{1}{k^n}=1$

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

complex even to you?

or me?

[willow skiff]

not for raijin

[hoary iris]

raijin? lol

[whole void]

how?

[whole void]

oh yeah like under the definition I had y = |x| would be differentiable at x = 0

[willow skiff]

yeah you just assumed differentiability

it happens

that's why these hidden assumptions (incl continuity) are super important

[whole void]

sorry wdym?

It just seems like it’s a kinda different definition, I’m not sure if that necessarily makes it wrong per say, but I’m not really sure

[river drift]

another problem is that you can have a function which is differentiable but crosses its tangent line infinitely many times in any open neighborhood of the point of tangency, e.g. x^2 sin(1/x)

[willow skiff]

ah I forgot about that

[whole void]

ohhh thank you for that

[noble lava]

It does have a tangent nevertheless

[whole void]

also u can’t rlly do calculation (or at least it’s pretty tedious) with the definition I had, is that also why it wouldn’t rlly be used?

[river drift]

a simpler but more fixable issue is tangent lines at points of inflection, which are above the function in one direction and below it in the other

but i think that the definitions are at least equivalent for twice-differentiable functions whose second derivative has constant sign in some open interval of the point of tangency

[whole void]

ohh yeah that is definitely a problem. how could u amend the definition though for that?

[river drift]

i had the idea of allowing it to be above on one side and below on the other, but upon closer thought that would clearly allow lines which just cross without tangency, so i'm not really sure

[whole void]

It does feel kinda odd like geometrically for sin(x) to have a tangent line at x = 0. I don’t think there’s a way to fix it then

like if u r using the “touch but doesn’t cross locally” definition

[river drift]

yeah. i think that the "touch but don't cross" notion seems to be a way of trying to enforce "pointing in the same direction" without explicitly invoking that notion, but the more we dig into it the less those seem to line up

[whole void]

wdym “those seem to line up”

I think what I had is equivalent to the touch but don’t cross but yeah there are differences with the calc definition

[river drift]

as in, touch but don't cross and the ordinary derivative definition (which attempts to directly formalize "pointing in the same direction") seem to match less under scrutiny

[whole void]

I think both are formalized. I think they have different ideas of course

[hoary iris]

Is $\frac{\sin x}{x}=\prod_{k=1}^{\infty}\left(1- \frac{x^2}{(k\pi)^2}\right)$?

[obsidian monolith]

Monkey•D•Luffy

[willow bear]

yes

[hoary iris]

Is $\prod(ab)=\prod(a)\prod(b)$? @willow bear

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

I think this works for the case of prod

right?

[willow bear]

well this is kind of horribly written but like

yes i guess

[hoary iris]

Which part of it is horrible?I mean correct me

how to perfectly write it

[willow bear]

i mean $\prod (a)$ is... vague

[obsidian monolith]

Ann

[willow bear]

i would have rather seen you write something like

$\prod_{k=1}^n (a_kb_k) = \prod_{k=1}^n a_k \cdot \prod_{k=1}^n b_k$

[obsidian monolith]

Ann

[willow bear]

something like this

also infinite products are quite finicky

[hoary iris]

,w finicky

[willow bear]

http://wiktionary.org/

look up unknown words there

[whole void]

wdym

[hoary iris]

Do we should take extra care to infinite products? @willow bear

[willow bear]

you should exercise extra care when dealing with infinite anything

not just products

[hoary iris]

may it be trickier than normal

[hoary iris]

I see

[whole void]

is there anything trickier about infinite products rather than sums?

[hoary iris]

@whole void Which grade are you?

[whole void]

11

[hoary iris]

,, \prod_{k=1}^{\infty}{\frac{(k+2)(k-1)}{k(k+1)}}=\frac{\prod_{k=1}^{\infty}(k+2)\prod_{k=1}^{\infty}(k-1)}{\prod_{k=1}^{\infty}k\prod_{k=1}^{\infty}(k+1)}

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

Can this be true? @willow bear

[willow bear]

no, $\frac{\infty}{\infty}$ is a bad idea

[obsidian monolith]

Ann

[hoary iris]

,, \prod_{k=1}^{\infty}{\frac{(k+2)(k-1)}{k(k+1)}}=\frac{\prod_{k=1}^{\infty}(k+2)\prod_{k=1}^{\infty}(k-1)}{\prod_{k=1}^{\infty}k\prod_{k=1}^{\infty}(k+1)}=\frac{k-1}{k+1}?

[obsidian monolith]

Monkey•D•Luffy

[willow bear]

ok no that's just very wrong

[hoary iris]

Is there any way to approach this?

[willow bear]

what, to calculate this infinite product?

[hoary iris]

yep!

[willow bear]

hm

there probably is but you won't like it

[hoary iris]

Just the approach is enough

[hoary iris]

I like every math stuff(cause I am an iron man lol)

[willow bear]

but i would look at the n'th partial product of that thing (ie instead of taking all the terms to infinity, look at the product of just the first n terms) and then cook up some magic with stirling's approximation formula

or whatever else is appropriate

maybe you won't even need stirling

maybe it can be done with just careful factorial bashing

[raw hill]

It telescopes tbf (assuming you meant to start from 2 instead of 1)

[willow bear]

that it might

[hoary iris]

,, \prod_{k=1}^{\infty}{\frac{(k+2)(k-1)}{k(k+1)}}=\lim_{n \to \infty}\prod_{k=1}^{n}(1-\frac{1}{^{k+1}C_{2}})?

[obsidian monolith]

Monkey•D•Luffy

[willow bear]

may be correct but i don't think it's helpful

[raw hill]

Did you mean to start from k=1 b/c the term for k=1 is equal to zero

[hoary iris]

I got this from that

lmao

[hoary iris]

Yes exactly

sorry for the mistake

[raw hill]

Yeah idk how this would be helpful for a telescope then

[hoary iris]

I got this prod from that comb lmao

Idk how to telescope it @raw hill

it is confusing

[modest bolt]

Π(k=1→n) k = n!

Π(k=1→n) (k+2)(k-1)/k(k+1)
= (n+2)!(n-1)!/n!(n+1)!
= (n+2)/n
= 1+2/n

idk if its correct or not but looks correct

[raw hill]

The product is zero for starting at k=1

Starting at k=2, it’s (n+2)/(3n)

[modest bolt]

oh

[raw hill]

$\prod^{\infty}_{k=2} \frac{(k+2)(k-1)}{k(k+1)}$

[obsidian monolith]

Civil Service Pigeon

[raw hill]

What id do here is notice that (k+2) and (k+1) differ by 1

As do (k-1) and k

So that’s where we’ll get the most “immediate” cancellation

You may not see what I mean rn, but it’ll make sense later

Because of this, I’d split the product up as follows: $$\prod^{n}{k=2} \frac{k+2}{k+1} \cdot \prod^{n}{k=2} \frac{k-1}{k}$$

[obsidian monolith]

Civil Service Pigeon

[raw hill]

Now, try writing out the first few terms of each of these products

And see what you notice

@hoary iris

[hoary iris]

Can we separate like this @raw hill

but can't for division

[raw hill]

Division is just multiplying by the reciprocal so …

$\prod a_k b_k=(\prod a_k)(\prod b_k)$ as long as everything is well defined

[obsidian monolith]

Civil Service Pigeon

[raw hill]

Which should be easy to see

[hoary iris]

then isn't this correct?

@raw hill

[raw hill]

.

[raw hill]

.

[hoary iris]

I see

[raw hill]

Ex. This infinite product is 1/3 (which I’ll let you work out later)

But $\prod^{\infty}_{k=2} \frac{k+1}{k^2}$ is zero

[obsidian monolith]

Civil Service Pigeon

[raw hill]

But by splitting the infinite product as you did, they’re indistinguishable

[raw hill]

This is why you generally do what Ann mentioned here with partial products/sums/…

Then take the limit

This way you don’t run into issues with orders of infinity in the middle of your process

[hoary iris]

What is partial products/sums?

[raw hill]

Basically what I did here

Find the general formula of the product up to the nth term

[willow bear]

uh

oh wait finite ones

mb

was about to say shit diverges

[hoary iris]

I'll try this and let you know(If I got it or not)

[raw hill]

k

[hoary iris]

one min or two min

[modest bolt]

what are you trying to do here? @hoary iris

[raw hill]

Probably what I just said (?)

Find the partial product by telescoping and then take the limit

[hoary iris]

trying to find that infinite prod

[modest bolt]

why making it hard, you can simply expand and see all terms cancel out and you left with 1/3

[hoary iris]

,, \frac{n+2}{3n}

[hoary iris]

Idu

@raw hill

I think I am done

@modest bolt Tell your idea btw

[raw hill]

That’s what I was going for with having them write out each product and observe the cancellation

Also so we can highlight the idea of taking the limit of a partial product to get an infinite product

Also I was breaking it down because

Yk they’re new to this

[raw hill]

Should be (n+2), not (n+1) in the numerator

[hoary iris]

this is working! isn't it?

[raw hill]

I don’t know what that’s supposed to show

[hoary iris]

from n=2

yes sorry

it is n+2

I mislatexed it

[obsidian monolith]

Monkey•D•Luffy

[raw hill]

And now to find the infinite product, we can take the limit of this as n goes to infinity

@hoary iris

What is that limit

[hoary iris]

from there i understand

1/3

[raw hill]

[hoary iris]

,, \prod_{k=2}^{\infty}{\frac{(k+2)(k-1)}{k(k+1)}}=\frac{\prod_{k=2}^{\infty}(k+2)\prod_{k=2}^{\infty}(k-1)}{\prod_{k=2}^{\infty}k\prod_{k=2}^{\infty}(k+1)}=\frac{2-1}{2+1}

It does work

right?

[raw hill]

For the reasons I said earlier, this is very abusive

But if you want to write this as informal scratch work that isn’t meant to be read

Go ahead

[hoary iris]

It is very hard to read but applicable

[hoary iris]

right?

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

which is 1/3

pigeoooooooooooon

@raw hill sorry for pinging you repeatedly

@modest bolt What are you typing so hard and didn't even sending?

[raw hill]

again, infinity/infinity is abusive

If you want to write it as scratch work, go ahead

But I’m not going to continue parroting back the same answer to you

[hoary iris]

I see

[raw hill]

Probably writing out their own method but it takes longer to write then it’s not in latex (I’m assuming this since their last msg also wasn’t in latex)

Probably going to be with factorials based on what they sent earlier

Which is fundamentally the same thing

You just “bunch” all the terms together before cancelling

[hoary iris]

ye

anyways, we can bunch the terms and cancel it in scractch work

there my problem done lmao

Thank you for you help! @raw hill and @willow bear

shubham I'll wait for your idea

ping me once you're done

[modest bolt]

Π(k=m→n) (k+l) = (n+l)!/(m+l-1)!

Π(k=2→n) (k+2) = (n+2)!/(2+2-1)! = (n+2)!/3!

You can rewrite others like this and see the whole product= (n+2)/3n

[hoary iris]

I want to say you something bro

You have a great ideas to explain

please latex them bruh

[modest bolt]

ok wait

[hoary iris]

not now

I'll read this now

from next

How the hell?

[hexed mulch]

wsp

[hoary iris]

gpt??

[hexed mulch]

I just joined

✌️

[hoary iris]

Happy sad journey here!

[hexed mulch]

Nah I HIGHkey like maths

[hoary iris]

Everyone does that before coming here lmao

[hexed mulch]

Dang

https://tenor.com/view/sad-sad-mario-mario-gif-18405221118743840924

[hoary iris]

but they would lost their hope

here

but dw

get help from shubham

lmao

[hexed mulch]

I'm 12 btw, so no weird shi 🙏

[willow bear]

uhhh

[hexed mulch]

However I am pretty good in maths

Just solved the 4d gaussian integral :)

[willow bear]

you're not allowed to be on discord if you're under 13, sorry mate

[hexed mulch]

I am 13 in 2 weeks?

[hoary iris]

ban him lol

[hexed mulch]

2. WEEKS

[willow bear]

dunno this is up to the mods

[hoary iris]

[hexed mulch]

I just joined 😭

[hoary iris]

You'll be muted for 2 weeks lmao

[hexed mulch]

are we deadess

[hoary iris]

fu-

[hexed mulch]

yes it was:
pi^2

[lyric meadow]

sorry, we can’t have you if you’re under 13

[hoary iris]

sad @hexed mulch

bye for now

@lyric meadow Will you add him after 2 weeks?

[lyric meadow]

they’ll be allowed to rejoin after 2 weeks.

[hoary iris]

Ok, Thank you!

What a strict rule lol?

I wanna test him with integrals

btw

[lyric meadow]

it’s discord’s TOS

[hoary iris]

so sed

[hoary iris]

I see

What if he lied that it is in two weeks?

[modest bolt]

did it

in latex

[hoary iris]

It is clearly not latex

lmao

[hoary iris]

I can see You forced gpt to get this result Lmao

after series of wrong results

[modest bolt]

it is i just pasted the latex in @obsidian monolith dm and uploaded the image here to not make it messy

[lyric meadow]

we just want to make sure that there’s not people who we know/have reason to suspect are <= 12 that are on the server. if they claim to be 13 then we have no way of verifying this but this is at least in line with tos of not willingly allowing people who claim to be under that age on the server.

[modest bolt]

i used gpt to turn my idea into latex

[modest bolt]

yea ai doesn't know what preamble texit has so it sometimes uses some extra package and texit can't render it

[hoary iris]

I see

Thank you for your explanation, smay!

[modest bolt]

if you think i copied the identity mentioned here from gpt, well i was making it here by using Π(k=1→n) k, what do you think i was typing for 10 mins

[hoary iris]

I see

Also @lyric meadow If I claim to under 13 eventhough I am 16, Will you mute or ban me?

[modest bolt]

she will if you ping her 3 more times claiming the same

[hoary iris]

You've got brain to derive identities

[hoary iris]

She*

[modest bolt]

mb

[willow bear]

fix the other pronoun too

[hoary iris]

lol

You sure don't like mispronouncing lol

[lyric meadow]

if you actually claim to be under 13 you will get banned yes.

[hoary iris]

Don't ban me lmao

I am 16

[modest bolt]

did you learn Π from your classes or online?

[hoary iris]

Nopw

my own little brain

understood

[modest bolt]

good 👍 me too 😂

[hoary iris]

it

It is easier than sum

I mean sigma

lmao