help-39

[warm elbow]

$a \in \bigcup {h_n(x) : n \in \omega} \implies \exists some h_n(x) \in {h_n(x) : n \in \omega} where a \in h_n(x)$

[jolly parrot]

toast

[warm elbow]

oops

so $a' \in a$ and $a \in h_n(x)$

[jolly parrot]

toast

[autumn fossil]

look ath the recursive formula for h now

[warm elbow]

\textbf{(a) Prove that for every set $x$, $TC(x)$ is transitive.}
\\
Let $x$ be any arbitrary set. Select $a \in TC(x)$ and $a' \in a$. So $a \in \bigcup {h_n(x) : n \in \omega}$. There exists some $b \in {h_n(x) : n \in \omega}$ such that $a \in b$. Call $b = h_{n}(x)$, where $n \in \omega$. By definition of $\bigcup h_n(x) = {z : \exists y \in h_n(x) \land z \in y}$. So by definition $a' \in \bigcup h_n(x) = h_{n+1}(x) \in \bigcup{h_n(x) : n \in \omega}$. Therefore $TC(x)$ is transitive.

@autumn fossil

[jolly parrot]

toast

[autumn fossil]

okay yeah, the idea is certainly right, ill double check the details (im kinda rusty with this now). But maybe it'd be a bit clearer if you used some theorems instead of refering to the definition everytime. Like surely you have proved that if a' ∈ a ∈ hn(x), then a' in U hn(x)

[warm elbow]

a' ∈ a ∈ hn(x), then a' in U hn(x)

i am not sure what theoreom this is

uhh

[autumn fossil]

its pretty much coming from the definition,
if x ∈ y ∈ A, then x ∈ U A

but ig that it doesnt really do any harm to write out the defns fully

its just hard to read, prolly bc of the latex

[warm elbow]

oh shit

[autumn fossil]

it will prolly look nicer on paper

[warm elbow]

yeah

but kk ty, this makes alot of sense

.solved

[pearl pond]

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[amber spire]

What am I doing wrong here, I believe no. of terms should be 41 for me to get the correct and with this approach…but why 41

[rough forge]

110275 seems wrong to me, they probably meant 11275 instead, also that it's 41 terms and not 40 terms is because when you do 66-26 you compute how much you need to go from 26 to 66, but you are not accounting for the 26th term itself, which needs to be considered as well.

[amber spire]

Yes
I see
Tyy

I can use this formula to calculate number of terms right:
(a-l)/n + 1

[rough forge]

there is a formula?

how does that wor

[jolly parrot]

Please give me something to evaluate.
See ,help calc for usage details.

Mar 11, 2026, 9:05 PM

[pearl pond]

@amber spire Has your question been resolved?

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[eager jewel]

have u tried anything

[thorn agate]

No

[eager jewel]

how about integration by parts

no wait let me try smthing first

[iron basin]

the solution i saw calculated f '(x) first

like $f'(x) = \int_0^{\frac{\pi}{2}} \frac{2x \cos^2 \theta}{\sin^2 \theta + x^2 \cos^2 \theta} d\theta$

[thorn agate]

Then

[thorn agate]

Wouldn't it be too long?

[iron basin]

like tan theta = t from there

[eager jewel]

yeah it is kinda long lowk but i think u can get somewhere w it

[steady vapor]

Pretty sure integration by parts would produce expressions harder than the original problem

[eager jewel]

well i took u=ln(..) and v=1
so what we integrate is basically
(theta)(tan theta)/(x^2+tan^2theta)

[steady vapor]

Which is more difficult...

[eager jewel]

but ur right this is not easy to integrate either

[thorn agate]

,, f'(x)=\int_{0}^{\frac{\pi}{2}}\frac{2xcos^{2}\theta}{sin^{2}\theta+x^{2}cos^{2}\theta}d\theta

[jolly parrot]

scoob

[thorn agate]

Ok so divide by cos^2

Wow

That was cool

It comes out be pi*something

Pi/x-1

So integrating that will give f(x)

[eager jewel]

its kinda not intuitive to calculate the derivative tho 💔

[thorn agate]

Fr

Interesting

So do i leave the answer in number + C?

[iron basin]

i mean this is like the one sum which i saw having this weird method

my package covered it too but i ignored it

[thorn agate]

Yh ts wont come

[midnight haven]

This is the infamous feynman trick afaik

[thorn agate]

@iron basin

Tysm

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[final shore]

so far I got that 72 = 2^3 * 3^2

i can't see how 4. contributes anything to the deduction

[midnight haven]

its more like a puzzle than math

[final shore]

math puzzle

[toxic remnant]

i suppose it implies that a newest model exists, there is only one youngest model

[final shore]

yeah

[toxic remnant]

a 3,3,8 case wouldn't hold

[final shore]

and there is also the fact that

whatever the sum is

it must be shared

with something like a 3,3,8 case

[toxic remnant]

2,6,6

is rhe same

3,4 collectively should imply that the sum is shared yes

[final shore]

so when they say the sum is 14

they were like mayb 2,6,6 or 3,3,8

but then they said newest

so they were like

[toxic remnant]

yes

[final shore]

oh 2,6,6

[toxic remnant]

yep

[final shore]

we got it

nice

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[midnight haven]

oh it was all about listing the factorizations then

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[untold swift]

How do you divide fractions?

[untold swift]

The other channel used letters and a bunch of stuff that’s impossible

The bot told me ai couldn’t even help and said not to use it

[jolly parrot]

@ruby cargo

[ruby cargo]

@untold swift

[untold swift]

Yes

[ruby cargo]

First: Do you know how to multiply fractions?

[untold swift]

No

I’ve heard you multiply top and bottom numbers but idk what that means

Ok now I do

[sterile python]

Long division is a great way if it cant be simplified normally

[jolly parrot]

@ruby cargo

[ruby cargo]

Does this make sense @untold swift

[untold swift]

Yes

[ruby cargo]

Aight

Second question: Do you know what a reciprocal/multiplicative inverse is?

[untold swift]

No

[ruby cargo]

Ok so

When you take reciprocal of a number

you basically interchange it's numerator and denominator.

I'll use the -1 in superscript to denote reciprocal for now (if you don't understand it for now don't worry, just know it means I'm taking reciprocal of the fraction) $\left(\frac 3 4\right)^{-1} = \frac 4 3$

[jolly parrot]

@ruby cargo

[ruby cargo]

Does this make sense?

[untold swift]

Yes

[ruby cargo]

Aight cool

To divide two fractions you have multiple the dividend with the reciprocal of the divisor

In other words

[jolly parrot]

@ruby cargo

[ruby cargo]

Does this make sense?

[untold swift]

Why’d division be multiply and only 5/8 is 8/5

[ruby cargo]

Do you remember how we defined division originally?

[untold swift]

A fraction

[ruby cargo]

Well a fraction is a way we represent a part of a whole

Which actually is identical to division

but it becomes a bit complicated if you take it that way because then you're thinking about dividing division and it may feel like a mess

[untold swift]

Is it opposite of multiplication

[ruby cargo]

Yes

It's the inverse of multiplication

to be more precise

Now, think of it this way, if I have a number say x, and I divide it by itself, what result do I get (assuming the number is not 0)?

[jolly parrot]

@ruby cargo

[untold swift]

1

[ruby cargo]

Correct

Now let's say I had a value y, which on multiplication (instead of division) with x returned 1

[jolly parrot]

@ruby cargo

[ruby cargo]

Multiplication with this y would always yield the same result as division with x

[untold swift]

Y is x but inverse

[ruby cargo]

Correct

it's the multiplcative inverse of x

aka reciprocal

Now think about this

[jolly parrot]

@ruby cargo

[untold swift]

The inverse. Y/x

[ruby cargo]

correct

and that's where we get it from

[untold swift]

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[bronze coyote]

I don't really understand what this question means

[hard tinsel]

LOLOL HAHAHA

maybe don't sleep in class next time

[bronze coyote]

yes

[pearl pond]

@bronze coyote Has your question been resolved?

[median swan]

Do you know how to sketch those sets in the complex plane?

[bronze coyote]

yes

i don't know what the arrows are meant to be

like z -> z^2

[median swan]

So if I'm not wrong all you have to do is just sketch them and then sketch the sets that you get by squaring each point in each set

[median swan]

That is simply notation, basically it tells you that f send the complex number z to z^2

[bronze coyote]

so its like f(z) = z^2

[median swan]

yes

[bronze coyote]

oh ok

i get it now

thank u so much

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[shadow elm]

how do i make sense of inverse of hyperbolic functions

[shadow elm]

oh wait

just componendo dividendo that

got it

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[shell brook]

you're welcome

[pearl pond]

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[crude parcel]

In 1. b is (-2,4) but is completely different in answers when drawn on coordinate system.

[crude parcel]

Answers:

[rough forge]

looks fine?

[tardy flicker]

b vector shows these changes ,
x position decreased by 2 and y position increases by 4

[tardy flicker]

i think she is thinking like -2i+4j should be the vector

[warped violet]

The vector doesn't mean the point (-2, 4)

You can move vectors around

[rough forge]

Oh i see

[warped violet]

In the answer image, they just moved it to the end of vector a

As the sum of vectors goes from the start of the first vector till the end of the last vector

The geometric idea

[crude parcel]

Then fucking what

[proper nova]

yo chill

[crude parcel]

I don’t understand this

[proper nova]

stop being rude 😭

[warped violet]

Uh

Have you learned about vector addition

Geometrically

[tame topaz]

Have you tried reading Linear Algebra Done Right by Sheldon Axler?

[midnight haven]

this is b vector from origin (position vector)

[rough forge]

vectors are spatially invariant, you can move them around, direction remains

is that a thing

[midnight haven]

-# they teach us vectors in physics before in maths hence i said idk i have 0 linear algebra knowledge

[tame topaz]

Oh I thought he meant an element of a free vector space

[midnight haven]

-# ignore me

[crude parcel]

But it’s 4 not 5.

[tame topaz]

Yeah stuff like position vectors aren't "spatially invariant" in classical physics since the reference point/choice of origin matters

But if you fix the origin then you can move them around

[warped violet]

What is 4 not 5

[pearl pond]

@crude parcel Has your question been resolved?

[tardy flicker]

a is 6,1 vector are not like permanently attatched from one point to another u can move them around and they are still correct

Its called vector translocation or transposition or smth i forgit

Forgot

So lets start from origin, add vector a to go to the point 6,1 now look at b, it says -2,4 meaning like u subtract 2 in x and add 4 in y

6-2,1+4

4,5

So if u start from origin and do a+b u get 4,5

Like u understand this like
Vectors are used to define positions
But positions cannot always define a vector

Like in this case,
Position/point 6,1 can be described by a vector
But a vector cannot be described by that point cuz like u can just move vectors however u want

[pearl pond]

@crude parcel Has your question been resolved?

[warped violet]

Uh

If you wish not to respond to our questions

You can .close you know

[rough forge]

took the 'you have the right to remain silent' too srs

[warped violet]

Unfortunately I am still in the process of mastering telepathy, so I can't help them without two-way communication just yet 🙁

[pastel umbra]

Skill issue, smh /s

[rough forge]

Maybe they believe in the super helpful legends, who knows...

[warped violet]

[pearl pond]

@crude parcel Has your question been resolved?

[crude parcel]

I’m gonna cry

[midnight haven]

cry

[sterile python]

Why is this?

[crude parcel]

I don’t understand nothing

[rough forge]

Can u tell us where you felt being left off? What's precisely your doubt?

[sterile python]

Don't understand nothing mean understand everything?

[midnight haven]

can you not just hop in randomly, post some message then disappear without answering questions

[pastel umbra]

You can't just say you "don't understand nothing", only to then keep disengaging the discussion

[crude parcel]

I’m busy, im in school.

[midnight haven]

you could have told so earlier

[worldly jewel]

Don't open a help channel if you're not available to engage with it

[warped violet]

I don't get it

Why react with an ❌ then to the bot

If you are busy

Even though there's like 5 people waiting to assist you

[rough forge]

queueing theory

[sterile python]

She dont want to collaborate...

[pearl pond]

@crude parcel Has your question been resolved?

[plush bramble]

sounds good

.close

[pearl pond]

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[pearl pond]

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[royal galleon]

So he says that finding primitives is easier than evaluating an integral. Then he says to find the primitive we read the differentiation formula backwards which gives us the primitive and then we evaluated this primitive at two endpoints. But isn't that what evaluating and integral means. Find its anti derivative and evaluated at upper and lower bounds

[summer imp]

I think he's referring to evaluating an integral as a limit of Riemann sums

[royal galleon]

he has never talked about the integral being the limit of riemann sums yet though

[summer imp]

How has the notation been defined then?

[royal galleon]

so he first defines partitions then step functions then he defines integrals for step functions as the area under the rectangles. Then he when he says we will look at the integral of a general function he says say we have two step functions s and t and then some function f. s <= f <= t If there exists only one I such that I is always satisfies integral s <= I <= integral of t then I = integral of f

then he adds some more stuff

and that is how he has defined then integral

[summer imp]

Well then that's what he's referring to

[royal galleon]

but then we have proven integration formulas

so I don't see how this is easier than using an integratino formula

[summer imp]

Doesn't he say that the integration formulas follow that paragraph?

[royal galleon]

yes he derives formulas that we have already derivied

is then not a mathematical question anymore but one of taste?

[summer imp]

It seems he's just explaining that those have been proves before from first principles but they come out of the FTC1-2 naturally without appealing to the definition

[royal galleon]

ok. I understand. thank you

.solved

[pearl pond]

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[shadow elm]

😀

i just want to check if my method is right

,rcw

[pearl pond]

@shadow elm Has your question been resolved?

[sterile python]

these 2 are definite integrals bro

they evaluate to constant not functions of x

@shadow elm i think you made mistake here

[shadow elm]

but xe^x

can come out of definite integral

[sterile python]

let the first integral be A, and the second one be B

than it should be f(x( = e^x + A + xe^xB

[shadow elm]

yes

thats what i did

[sterile python]

B here is a constant then

oh nevermind yeah i checked this is correct

👍

but this line i think sth off

y is just a dummy variable in the integral

should have just remove this line

[shadow elm]

i used integration by parts here

[sterile python]

.

I think this is unnecessary

[shadow elm]

how are you planning to solve the question then

idk any other way

[sterile python]

no you solved it correctly

i just suggest that the last line is not need

cross the last line would be nicer

[shadow elm]

😭

but its not solved without that line

[shadow elm]

see this

the original question

[sterile python]

i see

then its correct

[shadow elm]

but

🥸

[sterile python]

?

[shadow elm]

can u just tell me how i solve the ques

[sterile python]

i think let 2 of these definite integrals be A and B

then set up the system: $A = \int_{0}^{1} (e^y + B + Aye^y) dy$$B = \int_{0}^{1} y(e^y + B + Aye^y) dy$

[jolly parrot]

Minhh

[sterile python]

then solve for B?

[shadow elm]

e^y is not in the integral

wot

is this even

[sterile python]

it is i suppose

[shadow elm]

nvm

ill try later

.close

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[green aurora]

help pls

[sterile python]

!status

[pearl pond]

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

[green aurora]

it's a cosine

so the integral will be a complex sin

[jolly parrot]

Mr. Bumble

[green aurora]

so 0

because the area of ​​the cosine alternates between positive and negative

@sterile python

[pearl pond]

@green aurora Has your question been resolved?

[grave mirage]

Feynman ig

I(a,b)

[sonic patrol]

yeah you wanna use double integral magic here

$\frac{e^{-2x} - e^{-5x} }{x} = \int_2^5 e^{-tx} dt$

[jolly parrot]

Pseudo (Cat theory #1 Fan)

[sonic patrol]

so it's $\int_0^\infty \int_2^5 e^{-tx} dt dx$

[jolly parrot]

Pseudo (Cat theory #1 Fan)

[green aurora]

@sonic patrol @grave mirage so was I wrong?

[sonic patrol]

idk where you got this from

[grave mirage]

About what?

[green aurora]

I had shown my steps above

[grave mirage]

That is indeterminate

[green aurora]

its a complex cosine

euler's formula

[grave mirage]

Where did the sin term go?

[sonic patrol]

why are there complex numbers all of a sudden

x is real

[green aurora]

but can't we multiply above and below for j and then do the complex transformation?

[sonic patrol]

how

[shadow elm]

will be okay in the angle inside cos being imaginary

what year of college are you in

[shadow elm]

this seems fairly doable tbh

[sonic patrol]

i really don't understand why people are suggesting using trig for this

[shadow elm]

yea

double integral is the way

[green aurora]

then since it is real the term with the i is removed

[shadow elm]

yes ofc
dont you know double integrals tho

[green aurora]

yes

[shadow elm]

like this?

or you want to do it using trig

[green aurora]

but here there is only x

I made them with x and y

[green aurora]

this

[shadow elm]

how did u get here

[green aurora]

its a complex cosine

[shadow elm]

you mean hyperbolic cosine?

what is a complex cosine

,w cosh

[jolly parrot]

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[shadow elm]

this right?

[green aurora]

no

complex

[shadow elm]

🥲🥲 then im afraid idk

[green aurora]

but we can't use (f(0)-f(∞))*ln(5/2)?

[green aurora]

anyway thanks all!

i fixed

.close

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[pearl pond]

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[warped kite]

so i took the integral of acceleration got velocity +c added the initial and did it with displacement

and it says crosses why axis so i assume its x=0

is this right?

[shell brook]

yes

[warped kite]

ok

ty

!close

.close

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[quick venture]

for this would be multiply the series together?

[main oriole]

period for multiplication 🤮

but yeah

[quick venture]

and then add the terms that are similar?

or simplify

[pseudo oxide]

yes

[mortal seal]

Yup

As tan has no constant term, you can just develop e^x to order 3 instead of 4 btw

[verbal whale]

Yeah it's horrible for me too

[pearl pond]

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[quick venture]

im not sure where to start with this question

[plush bramble]

Does {.} Mean decimal part

[quick venture]

im not sure

[rough forge]

idts

[midnight haven]

Does it mention

[timber tartan]

taylorreihe

[quick venture]

the answer is -1/10

[timber tartan]

,w taylor series of sin(x)

[quick venture]

so a fraction

[jolly parrot]

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[timber tartan]

,w taylor series of cos(x)

[jolly parrot]

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[timber tartan]

neglect x^4+ terms

[quick venture]

so i find sin^2x?

[timber tartan]

you square (x - x^3/6)

that will be some x^2 + x^6 - x^4

idgaf about constants since im neglecting all x^4+ terms

so it reduces to just x^2

[quick venture]

,w (-x^3/6)^2

[timber tartan]

similarly, cos^3(x) = (1-x^2/2)^3

,w expand (1-x^2/2)^3

[jolly parrot]

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[timber tartan]

we are left with -3x^2/2 +1

so all in all

[quick venture]

hmm

[timber tartan]

the limit becomes 1 - 2x^2 + 3x^2/2 - 1 / 5x^2

[quick venture]

i thought we find sin^2x and cos^2x and sub into the numerator

[timber tartan]

or -x^2/10x^2

or -1/10

[timber tartan]

no, you remember that sin(x)'s series is x - x^3/3!

i mean yeah

the idea is that

just do the sub carefully

and disregard all terms over x^4 for simplicity

it will reduce to a neat form

try it out!

[quick venture]

not sure if this is what you mean

[rough forge]

just use lhopital

[pearl pond]

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[storm parcel]

how do i find the missing zeroes?

[sterile python]

!status

[pearl pond]

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

[sterile python]

What have you done or think of so far

[fossil pine]

hello everyone im new here

[sterile python]

Hi

[fossil pine]

hello

[sterile python]

Please dont chat here if not helping

[fossil pine]

sorry i didnt know that part

[pearl pond]

@storm parcel Has your question been resolved?

[storm parcel]

oop

[storm parcel]

1

[storm parcel]

i tried plugging it in but idk how to solve for the other zeroes

[candid wren]

😐

i know wht u feel pal

[storm parcel]

this is algebra 2 writing equations of a polynomial btw

[sterile python]

so, what can you conclude from the vertex?

given that this is (-1,16)

<@&268886789983436800> SCAM

@storm parcel what do you think?

[storm parcel]

maybe that the second root would be 2 since a parabola is symmetrical?

[sterile python]

notice the -1

this is the horizontal coordinate of -1, this is the symmetrical axis

<@&268886789983436800>

scam again

[pearl pond]

@storm parcel Has your question been resolved?

[storm parcel]

ohh you’re right

okay nvm

or idk

OH i get it

so -1 is like the axis of symmetry so the next point has to be the same distance from -1’s line

[sterile python]

Then if the first solution is x=-3

It is 2 units to the left

Then, what is the other point?

[sterile python]

Correct

[storm parcel]

x = 1?

[sterile python]

Correct

Now you got 2 points, can you find the formula now?

[storm parcel]

i’m not sure how to put it in standard form

[sterile python]

So you have ax^2 + bx + c = y right

But you already have 3 points (1,0), (-3,0) and (-1,16)

Substitute in x y values and find a b c

[pearl pond]

@storm parcel Has your question been resolved?

[storm parcel]

oh okay

i wasn’t sure if it was that one

do i need y intercept?

[sterile python]

lol

if a point is x intercept then y value automatically 0

[pearl pond]

@storm parcel Has your question been resolved?

[pearl pond]

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[sharp smelt]

I have no idea tbh

The only idea I had was to integrate this over R and show its considerably more than 1, but on second thoughts that doesn't help

wait is it simply that this is a product of probabilities which is.>1 at certain poingts>

[wet osprey]

i mean

surely it has to do with the fact that what do you do when theta is non-positive

like what does it even mean if i let theta = 0 and then my likelihood is identically the 0 function everywhere

[sharp smelt]

I see

that makes more sense

thanks

.close

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[heavy phoenix]

Anyone free to help

[dusty jungle]

yeah just ask away

[heavy phoenix]

Ik the line is 180

I originally thought y was 40

And x was 70

But chat gpt n google says it’s wrong

And I don’t understand how they re doing it

[oak sinew]

Hint: angles in a 4 sided shape add to 360 degrees

[nocturne plover]

Also do you know about F and Z angles?

[heavy phoenix]

No..

[surreal ore]

And the remaining angles is same as as angle x

[heavy phoenix]

Oh u mean like

How

The transversal angles are same?

[crystal basin]

are arrows supposed to highlight parallel lines?

[nocturne plover]

yes

[heavy phoenix]

Yeah

[heavy phoenix]

Yes I do

[heavy phoenix]

What now

[nocturne plover]

x can be found by using what giraffe said and Z angle

[surreal ore]

Lk z angles are equal

[heavy phoenix]

Alr I got itt

Thanks guys

[tardy flicker]

Do .close if you are done btw

[heavy phoenix]

.close

[pearl pond]

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[vapid stump]

wht is derivatives

[final shore]

you ask a deep question

[summer imp]

Any questions in particular about them? If not then it's a bit hard to conduct a course in calculus in a help channel

[vapid stump]

why they work the way they work

why they determine how steep a hill is

[summer imp]

The main idea is that if you're given two points on a curve you may compute the slope of a line joining them

If you get those points close together, you get a better and better approximation of the steepness at a point

[mystic bronze]

Just briefly, it’s a function that is “derived” from some function, that tells you how quick that function changes at any specific point

[vapid stump]

yeah but why

[dusty flame]

its like reading a speedometer when driving a car

[dusty flame]

lots of application

u find this a lot in the entire of field of science

[vapid stump]

yeah but why does it determine the speed of my car

[summer imp]

Are you asking why it's done or why it works?

[vapid stump]

why it works

[vapid stump]

y cant a book determine the speed of my car or a basketball

[summer imp]

What

[vapid stump]

yes like why cant a ruler determine the slope or carbon fiber why derivative

[sweet oxide]

Just watch that video https://www.youtube.com/watch?v=9vKqVkMQHKk&list=PL0-GT3co4r2wlh6UHTUeQsrf3mlS2lk6x&index=2

even mentins the car example

[vapid stump]

depends how long is it

16 mins thts not long

[dusty flame]

MOD

thx

[vapid stump]

y wht he do

[sweet oxide]

how does writing MOD in capital letters call a mod instead of pinging one??

[dusty flame]

funni

[wild wren]

Before you guys invest in this I just wanna leave this here
https://discord.com/channels/268882317391429632/1482474916539531489

[sweet oxide]

lol

yeah no I see going from basic multiplicatoin to calculus in a day is quite the leap

[foggy scarab]

well think about it this way, you know how a slope is in form of change in y/ change in x

now make x smaller and smaller, finally you will get a elemantary x (called dx) which makes change dy (elementary change in y), this is what derivative is (dy/dx)

coming to velocity same logic but y is distance/displacement and x is time

[mystic bronze]

You can determine the slope by a ruler tho

Divide the y change by the x change

Measure with ruler

[vapid stump]

yes but why derivative

[foggy scarab]

now you might ask "why cant we just put y/dx and consider a significant change for dx" , well because it is basically in finite/ 0 for which will give infinite

[vapid stump]

im still confused

[foggy scarab]

see, now you will be given some y = function representing location with respect to time t

[vapid stump]

like why is it derivative

[foggy scarab]

or y = f(t)

[mystic bronze]

Wdym why derivative

[foggy scarab]

now

[mystic bronze]

Explain the concern deeper

[vapid stump]

why is it derivative

[mystic bronze]

What

Try to explain to me what a function is

If you know

[foggy scarab]

what is velocity, change in location by change in time, but for elementary change in time , we have elementary change in x, and hence we end up with v=f'(t)

[vapid stump]

why a derivative y not a ball a ruler or a keyboard or a speedometer

why derivative

[summer imp]

Well you don't have a speedometer or ruler on your function

[foggy scarab]

derivative is the name of the method

can you measure an infintesimally small thing with anything?

[vapid stump]

input change output

[vapid stump]

no but why derivative

[vapid stump]

no but maybe u can

[foggy scarab]

this is where sir god chad (maybe idea stealer) newton came up with this logic, for which the change is so small, not even anything can measure it

[summer imp]

If you're given a function f(t) giving your position in time, you may consider taking the average velocity between two points

[vapid stump]

why cant anything

[summer imp]

This is the slope between two points

[foggy scarab]

well, if u can measure 1/infinity, you can measure infinity, which itself is wrong

[foggy scarab]

because this is the logic sir made it for

[summer imp]

The derivative is what you get when you take the average velocity and take it between closer and closer points

[vapid stump]

ik but why is it derivative

[vapid stump]

why not another logic

[summer imp]

Effectively giving you the velocity at a point and not between two points

[vapid stump]

yes but why derivative why not a pea

[foggy scarab]

am not following what u tryna say now....

[summer imp]

It doesn't seem like you're asking and trying to understand it in good faith

[foggy scarab]

pls elaborate what you tryna say

[vapid stump]

i am but yall tryna make me understand something else rather then answer the wuestion

[mystic bronze]

@vapid stump don’t repeat your question, say exactly what you don’t understand

Wdym “why it’s a derivative”

[summer imp]

Because "why the derivative" is a weird question to ask if you don't know what a derivative is in the first place

[vapid stump]

i dont understand derivative why cant it be a pea or a speedometer etc why is it a derivative

[vapid stump]

ik wht it is

[summer imp]

Well it doesn't seem like so because then you wouldn't be comparing it to a pea

It's called a derivative that's the name of the process

[foggy scarab]

well @vapid stump , try to find the length of perimeter of a circle using scale only (NO formulas allowed) you will see the issue

curved lines are made up of elementary straight lines, but if the straight lines arent elementary (like how you are saying why not a pea) then it is no longer a circle, it is a polygon

[vapid stump]

i can compare it to a pea i can compare ur atoms to a pea

[smoky gull]

look i call ^2 a sqaure function, |_| aboslute value function similarily we call rate of change of a function wrt to the variable as differentiation

[smoky gull]

okay this is just a troll help

please use this server in good faith

[summer imp]

Again I don't think you're asking in good faith

[vapid stump]

why cant the perimeter bend and form

[vapid stump]

i am

its hard to understand

[foggy scarab]

wdym bent and form?

[smoky gull]

i would suggest you to rethink your Question or maybe try to seek more detailed explanations on web

[vapid stump]

why cant the straight line bend into a circle or any other shape

[smoky gull]

If there are parts in those texts which you do not understand go ahead and message ehre

[foggy scarab]

bro...., which grade are you in

[smoky gull]

for now i think this is a ragebaiting conversation

[vapid stump]

does tht rlly matter

[foggy scarab]

guys @smoky gull wait maybe he is in a lower class

[foggy scarab]

a teacher irl would be much more helpful than us

[vapid stump]

oh yall are very helpful yall just dont understnad my question yall are not escaping logic

[foggy scarab]

you will understand that the definition of straight and curved lines, and straight line are "straight " not curved, you cannot just say curve it like a rope

[vapid stump]

but why cant it bend and form

[final shore]

a straight line can bend

u just gotta bend it

[foggy scarab]

well , you need to have a certain idea before talking with us, most of us are in a class above you i guess, which makes it difficult for you to understand what we are saying since you haven't learnt the basic yet

[final shore]

it won't bend without a bending action

[vapid stump]

yessssssssssssssss

[foggy scarab]

what will bend it mathematically? explain

[smoky gull]

as i said

[foggy scarab]

it aint like a bamboo pole that you can magically bend

[vapid stump]

maybe an unidentified force

[vapid stump]

i mean like why sphere

[foggy scarab]

@vapid stump pls focus on your current class, when time comes you will understand much better than now

[foggy scarab]

sphere is made of elementary planes, not a bent plane, pls

[vapid stump]

no i cant sleep without figuring this out

[foggy scarab]

keep it to rest for now, when time comes you will understand

[final shore]

mobius transformation

[vapid stump]

aint plane a 2d shape

not 3d

[sweet oxide]

he asked yesterday how basic multiplication like 5*5 work ?

[smoky gull]

okay yeah thats thats not getting in his head if hes asking whats is derivatives

[foggy scarab]

that is basically using elementary vectors and adding, not valid

[mystic bronze]

What pea

[final shore]

guys this is clearly an etymological question

[vapid stump]

nothing just a concept a name an object

[mystic bronze]

Derivative is a tool in math that very easily gives us the slope at any point

[foggy scarab]

@vapid stump ask this to mit professors, we aint advanced enough

[mystic bronze]

Derivative is also a function like you said, input and output

[sweet oxide]

how did u even went from basic arithmetic to calculus in a day

[final shore]

maybe we should list the zfc axioms for him

[vapid stump]

idk

[mystic bronze]

Though the input is the x value, and the output is the slope of the original function at that point.

@vapid stump

This is the basic answer to your question

[vapid stump]

i just ask why a derivative

[foggy scarab]

yall let him rest he will figure it out later, youtube exists for a reason

[sweet oxide]

do u know the formula: (y_2 - y_1) / (x_2 - x_1)

[mystic bronze]

There are ways to compute a derivative

[foggy scarab]

youtube will help

[mystic bronze]

@vapid stump

[sweet oxide]

to calculate slope?

[foggy scarab]

now close this channel @vapid stump youtube will teach it better trust me

[vapid stump]

slope form

[sweet oxide]

just watch the video I linked

[vapid stump]

im good ty tho

[vapid stump]

ok

[sweet oxide]

can we ban this guy?

[vapid stump]

y

[mystic bronze]

Don’t be harsh

[vapid stump]

wht i do

[mystic bronze]

Everyone started somewhere

[vapid stump]

for existing

newton asked deep questions why cant i

[mystic bronze]

Fin if you are actually interested, you will be able to learn it

[vapid stump]

he asked why does an apple fall but not the moon

[mystic bronze]

Just start from the ground up

[vapid stump]

i did i learned multiplication

[foggy scarab]

i started by figuring out that there was a switch (button) in the fridge which turns of the light in the fridge, was crazy experience ngl

[mystic bronze]

Derivatives isn’t the next step…

Do you know division?

[foggy scarab]

yall let him watch the vid

[mystic bronze]

What’s 12 divided by 3

[vapid stump]

inverse operation of multiplication

yes

[mystic bronze]

Great

[vapid stump]

i do

[mystic bronze]

Do you know powers?

[vapid stump]

wht tht

[mystic bronze]

2 to the power of 3

For example

Like this $2^3$

[vapid stump]

idk division still kinda hard

[jolly parrot]

kizner

[smoky gull]

i am surpried bro didnt say batman or superman

[vapid stump]

2 x 3 6

[mystic bronze]

😭😭

[vapid stump]

it 6

[mystic bronze]

No

[vapid stump]

huh

how

[smoky gull]

@vapid stump i cant just jump straight to writing essays without learning basic tenses right?

[vapid stump]

no

i can tho

pretty easy if u pour ur heart and soul into it u could

[smoky gull]

similar logic here, you have to start from baisc, (and there is no shame in tht) and slowly work your way upto the tougher problems

[mystic bronze]

Also ChatGPT can help you really

Ask it questions it will answer

[smoky gull]

okay this is just annoying now

<@&268886789983436800>

[vapid stump]

chatgpt in with the military i prefer copilot

now

[mystic bronze]

What military

[whole valley]

whats up

[vapid stump]

wht i dp

wht i do

[sweet oxide]

do u like roosters?

[foggy scarab]

you willnt wrote essays if you hasnt knew tense

see the problem eh?

[smoky gull]

i tagged mods not you sorry

[vapid stump]

huh

[whole valley]

ok rude

[vapid stump]

u cant right

[mystic bronze]

Ma kore akhi

[foggy scarab]

exactly, hence without knowing tenses, you cant write an essay, unless you want a 0 for it

[sweet oxide]

I agree that it can help explaining scuh kinda stuff but I dont like that it then goes on to pretend ur some kind of super genius so Im not sure how helpful that is

[vapid stump]

but who says u have to

[smoky gull]

@sharp vigil could you please take action (sorry for the ping)

[vapid stump]

morse code

so tht dont really apply

[foggy scarab]

buddy at this point just watch the vid 🥀

[vapid stump]

k

[mystic bronze]

“Explain like I’m 5”

[mystic bronze]

No way

The biggest ragebait of our generation

[sweet oxide]

no u dont understand, writing with others for 3 hours trying to understand anything takes significantly less time then watching a 10 minute video

[vapid stump]

nuh uh

im not a ragebait

[mystic bronze]

Where did hear about derivatives

And how old are you

[foggy scarab]

bro the more you write, the more you remember you know what they say

[vapid stump]

idk and idk

[mystic bronze]

😔

[vapid stump]

why not call newton stupid since he asked why does an apple fall

[mystic bronze]

What

You’re not stupid

[radiant terrace]

How is this a productive thing to say?

[foggy scarab]

lets leave him alon in peace bro 🙏 let him see the vid pls 😭

[radiant terrace]

To your question of why derivatives work to define things like speed and velocity, these words are defined in terms of the derivative.

[vapid stump]

idk pls dont mute me again

[vapid stump]

tht was not my question

but thanks

[radiant terrace]

The q in the pin seemed like it was asking that?

[foggy scarab]

doot let him see the vid trust his doubt will be solved 🙏

[radiant terrace]

Can you rephrase your q for me?

[vapid stump]

yall make it sound like im stupid

[vapid stump]

why derivative

[mystic bronze]

No

[radiant terrace]

Why not? Be more specific.

[mystic bronze]

No one in history learned derivatives before powers

[copper sigil]

what grade are you in @vapid stump ?

[vapid stump]

why cant it be a pea

[vapid stump]

idk

[radiant terrace]

Why can't + be a pizza?

[copper sigil]

Okay, how old are you?

[mystic bronze]

He won’t answer

[radiant terrace]

If you ask questions with no real point to them you probably won't get very good answers.

[vapid stump]

idk but it can if u cut it into a shape of a plus

so why derivative

[radiant terrace]

Are you wondering why we study derivatives at all or something else?

[vapid stump]

no just why derivative

[radiant terrace]

Ah okay. Well if you're asking troll questions to waste peoples time I should just mute you.

[mystic bronze]

Why bother making these sentences

[foggy scarab]

yo fin, why are we called human why not rock, because the rock is called the rock......

[mystic bronze]

Just understand what we tell you

[vapid stump]

im not tho

[mystic bronze]

No one is against you just make it easier for us

[vapid stump]

idk but we can be called a rock

[radiant terrace]

Okay. so then elaborate more on your question

You can ask why about anything.

[mystic bronze]

No we don’t

Can’t

[radiant terrace]

Clearly just saying why for no reason isn't so productive.

[vapid stump]

why cant it be something else like a pea or an apple or atom why derivative

[foggy scarab]

you dont need mathematical guidance, you need philosophical guidance, pls this is not related with math, this is related to philosophy

[mystic bronze]

Bro

What

An apple can’t calculate slopes

[radiant terrace]

Because words are arbitrary. We pick words to refer to things. The actual words/sounds we use are less important than the thing they represent.

Why don't we call cats dogs instead?

It would be confusing and hard to communicate if we did

There's not much of any other reason for why not.

[foggy scarab]

why is why why and not whynt or whyied

[radiant terrace]

This is true

Not really a math q

[foggy scarab]

structure of english my guy, who found it gets to name it

[mystic bronze]

Are you asking why is it called a derivative? @vapid stump

[vapid stump]

math is probability not just facts u can say u have a hand but not with upmost certainty u can say u have a hand but be 99.9999% sure but not guaranteed

ur hand could be a apple

[radiant terrace]

Math is different from empirical sciences.

[vapid stump]

maybe ur brain is playing trick on u

[radiant terrace]

Math is based on the axiomatic method.

[foggy scarab]

doot do the honors, pls give him the treatment

[radiant terrace]

You make a set of base assumptions called axioms. You derive new things via logic from those assumptions.

[foggy scarab]

salute of 21 cannons

[radiant terrace]

The things that happen in the real world are somewhat irrelevant to that process

[shadow elm]

did bro watch that holder's uncertanity principle video or veritasium 😃😃😃

lmao

[radiant terrace]

With the exception that sometimes we like to build logical/mathematical models of irl things using math.

[vapid stump]

i did actually

[shadow elm]

clearly you did

[vapid stump]

no why is it a derivative

[radiant terrace]

Again, if you're going to waste time asking why pointlessly and not elaborating your question I'm just gonna assume you're trolling.

Last chance :^)

[shadow elm]

wdym by a derivativer lmao

[foggy scarab]

fin are you fin or are you a fin of fish who is controlling fin ? pls no brainrot answer

[foggy scarab]

parth bhai chod yaar isko nhi pata he ye ese hi kuch bhi bol rha he

[vapid stump]

im fin cuz i chose tht name

[radiant terrace]

Still not elaborating the question

[vapid stump]

i did elaborate

[radiant terrace]

Not really

[vapid stump]

kinda really

[radiant terrace]

I guess your trolling. Everybody wave bye to fin while they take a break for a bit.

[foggy scarab]

no technically why arent you a fin of a fish?, why are you a human rather than the fin? you are technically a fish

[vapid stump]

wht

[shadow elm]

what is the question again

[foggy scarab]

aight salute comarade 🫡

[radiant terrace]

Going forward don't ask troll questions when you come back.

.close

[pearl pond]

Channel closed

Closed by @radiant terrace

Use .reopen if this was a mistake.

[pearl pond]

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[austere wraith]

guys im first year into high school just did quadratics and basic trig and inverse trig by myself what should i do next

[shell brook]

You can start calc

Or learn basic combinatorics

[austere wraith]

calcuslus at year9??

also whats combinatorics

[rough stream]

Combinatorics is the study of "how to count the number of things"

For example, let's say there's 10 cards. You want to make a hand of 3 of those cards. How many ways can you do that?

[grave mirage]

Basic set theory, functions and relations, Combinatorics, elementary number theory and binomial expansions then limit, continuity, differentiability (LCD) and sequences and series, then calculus till calc 2 and ordinary differential equations, then probability and stats, then linear algebra,PDEs and vector algebra/geometry, then calculus till calc 4 then analysis ig

Depends

[pearl pond]

@austere wraith Has your question been resolved?

Channel closed

Closed by @austere wraith

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[magic bolt]

Is symmetry a transformation that renders object identical looking or the object itself ?

[worldly jewel]

the example you gave is one kind of symmetry but the term can refer to something broader

or the object itself ?
I don't know what you mean by this

[magic bolt]

This is what I saw

"used to refer to an object invariant under some transformation"

This was slightly different from my earlier understanding of symmetry

Which was it itself being a transformation

Which renders some object invariant

[worldly jewel]

I think the difference is that "objects" (by which I assume you mean 2D or 3D geometric figures) in this new definition are subsumed into more abstract things

for instance, a square and a circle have symmetries, but an equation can also have symmetries

[magic bolt]

Sure

But that still doesn't uhh

Fit in

Because here it says that object whatever it maybe

Is invariant under a transformation

But I was under the impression that the object we are talking of (symmetry) is itself a transformation

Because here they refer to symmetry as an object

Which I always thought was a transformation

Or are they subsuming transformations themselves under this definition of "object"?

[worldly jewel]

yes there is no reason you can't think of transformations themselves as objects

[magic bolt]

But then

What do you mean the transformations are invariant under transformations

What meta transformations are they talking about here

[worldly jewel]

[magic bolt]

Huh

They say "is usually used to refer to an object that is invariant under some transformations"

And if that object itself is a transformation

[worldly jewel]

well no

what they mean is we can say that object has a symmetry

it is not the symmetry itself

it's just wording issues

[magic bolt]

So my earlier understanding of symmetry being a transformation that renders object invariant

Is right?

[worldly jewel]

it is roughly correct

[magic bolt]

Can you smoothen the rough edges

[worldly jewel]

you should talk about a transformation being the symmetry of an object

the two are tied

[magic bolt]

What's "the symmetry of an object"

[slim escarp]

the set of transformations that is invariant

[worldly jewel]

well informally it is just the transformations that leave (some properties of) the object unchanged

[magic bolt]

How can a transformation be a set of transformations

[worldly jewel]

my point was when you talk about a transformation being a symmetry you have to say what it is a symmetry of

[slim escarp]

symmetry isn't a transformation wdym

[worldly jewel]

I think this is just a wording issue I guess kmu interpreted your question as "what are the (set of) symmetries of an object"

[magic bolt]

Well tl give you some context, I am starting out with group theory basically, so I want this idea of a symmetry clear in my head

[slim escarp]

oh

[pseudo oxide]

a symmetry is a transformation that leaves some property of an object invariant, yes

[magic bolt]

Yeah

[pseudo oxide]

e.g. the dihedral groups preserve the vertices of a polygon

[magic bolt]

That definition and this one I am not able to reconcile

[pseudo oxide]

-# not sure if thats the best way to phrase it ngl
yes i saw your image

[magic bolt]

Yeah

[slim escarp]

they are isomorphic

[pseudo oxide]

…?

[slim escarp]

its just colloquial

[worldly jewel]

if you know about groups, a symmetry of some object S with some properties φS we care about is an action of G on S that leaves φS unchanged

[glacial bluff]

I've pinned that image because I've seen it like three times throughout the channel, so you can refer helpers or yourself to pins if necessary.

[pseudo oxide]

did you just say the definitions are isomorphic

[slim escarp]

yes

[pseudo oxide]

thank you bina !!

[worldly jewel]

I think for some reason you keep getting tripped up on minor language inaccuracies

[magic bolt]

Right

[pseudo oxide]

the object itself is not a symmetry

[magic bolt]

Not sure what you mean

[pseudo oxide]

the transformation is a symmetry

[magic bolt]

Right

[pseudo oxide]

yes

what exactly

are you confused abt

[magic bolt]

Im confused as to what this wikipedia on symmetry is saying

[worldly jewel]

Like for example here it says "Symmetry ... is usually used to refer to some object with ..."

[pseudo oxide]

this definition is incorrect, as it says the object that is invariant etc etc is a symmetry. that is wrong

[magic bolt]

The one which is pinned

[worldly jewel]

What it meant is that "we say the object has symmetries when ..."

[pseudo oxide]

go to the wiki for group theory instead

[worldly jewel]

but it's just a minor language bug

[magic bolt]

Ah ok that's what I wanted to get clarified

[worldly jewel]

the object is not literally the symmetry

[magic bolt]

Yeah that's what I thought

[pseudo oxide]

e.g. a CIRCLE has rotational symmetries — rotate it it stays the same

the circle itself is not the symmetry

the symmetries are the rotations

acting upon said circle

[magic bolt]

Yup

[pseudo oxide]

a set with these symmetries

[magic bolt]

That clears it up

[pseudo oxide]

that has inverses, identities, and compositions, and is closed

is known as a group

[magic bolt]

Right

[pseudo oxide]

in this case, the group of 2d rotations is U(1) on S^1, depending how you look at it

[worldly jewel]

minor sloppiness in language like this shows up very often and it's best not to get stuck on them

[magic bolt]

So any time we take all transformations that are symmetries and keep them in a set

We have a group?

[magic bolt]

Acting on the same object

[slim escarp]

it has to form a group

[pseudo oxide]

and ensure that

• they are closed; you can’t escape from the set by applying a bunch of symmetries
• you can compose two symmetries to get another one in the same set
• there is a symmetry that doesnt change anything (the identity)
• there are inverses of each symmetry which reverse each symmetry

[worldly jewel]

the requirement that it be a group is a part of the definition of what a symmetry is

[pseudo oxide]

these form the grp axioms

jesus i hate phones

anyway

!done

[pearl pond]

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

[magic bolt]

What I mean is that if we have an object invariant under some transformations, and we take the set of those transformations with operation of composing these transformations will it always naturally folllow the group axioms?

[cinder flower]

the symmetry group of an object is, as expected, a group

[pseudo oxide]

not rlly what helpee asked

[slim escarp]

inverse don't necessarily follow i think

[cinder flower]

[slim escarp]

you'd need the transformation to be invertible