serious-discussion

[serene pulsar]

So now I get to take Calc 1 like I wanted

[cyan goblet]

it’s me im an alien

im an alien ama

[long matrix]

<@&268886789983436800>

[serene pulsar]

Man I'm so psyched I aced my test. I really appreciate all the people here that helped me when I was stuck or needed to understand something.

And I'm so excited to register my classes

[deep mango]

Woooo

Good work

[nocturne skiff]

1 month for results to be released

for me

[ocean harbor]

pog

[chilly hull]

[split pawn]

I thought it was a job placement.

All the fun has ended.

[serene pulsar]

Haha the fun will begin again when I'm in Calc 😄

But for now I'm going to take a break to relax, because the last 2 weeks has been 8 hours (8+ on some days) of studying per day.

[neat lintel]

this statement, it seems the best the part (for me) atleast

idek you but reading that made me happy and i smiled

[serene pulsar]

Thank you!!!
It is the best feeling I think. I have a lot of fun studying too but it was starting to get stressful haha.

[split pawn]

Have you seen Indian students

But yeah, congratsie

[mint patio]

What are other cool natural science fields to learn about besides physics and maths?

Chemistry sort of interests me

Biology not so much, but maybe

Not sure what else

[split pawn]

Well physics interests me.

Nothing else.

[neat lintel]

Agricultural science
Agronomy

[mint patio]

That’s a science? Doesn’t that just fall under, like, botany? 😭

Idk

Like a mishmash of other sciences

Is what I meant

Wtf is agronomy

[loud snow]

You are missing out

[mint patio]

I’m sure

Just not that interesting to me

[onyx marsh]

:0

[neat lintel]

$$\int_3^\infty \frac{4}{x^2-4}$$

[fathom swallow]

Brandon H

[neat lintel]

$$4\int_3^\infty \frac{1}{x^2-4}$$

[fathom swallow]

Brandon H

[neat lintel]

$$4\int_3^\infty -\frac{1}{4}\frac{1}{1-\frac{x^2}{4}}$$
$$-\int_3^\infty \frac{1}{1-\frac{x^2}{4}}$$

[fathom swallow]

Brandon H

[neat lintel]

oh i messed up

[fathom swallow]

Brandon H

Brandon H

Brandon H

[flat harbor]

use the fucking latex channel lmao

[solid snow]

what exactly is being discussed here

also its wrong

[mental stratus]

there's a goddamn #latex-testing channel for you

[long matrix]

brandon thinks hes below none and above all.

dont question

[solar hawk]

fr bruh

thats actually so annoying he always does that shit

[proven knoll]

$x$

[fathom swallow]

beijing beef

[nocturne skiff]

what does beijing beef mean

[lavish scaffold]

Does anyone here have TI-nspire CAS calculator or Casio class pad?

[analog hedge]

tell me what does the modulus function do

like i dont get it

modulus is a function?

why

[storm sage]

it inputs something and outputs the length of that thing

[analog hedge]

example

you put modulus of -1 = 1

[storm sage]

Yes

|-1| = 1

[analog hedge]

ye

but how negetive distance

[storm sage]

No it's the distance of -1 from 0

On the number line

They are 1 unit apart

[analog hedge]

ok

[storm sage]

So |-1| = 1

[analog hedge]

how do you define this fuction

*function

like mathematically

[storm sage]

|x| = distance between 0 and x

[neat lintel]

ayo shuri get off dick

[long matrix]

[neat lintel]

I've obviously deleted my messages hours before

[long matrix]

cope

seethe

writhe

[neat lintel]

Go running

[neat lintel]

why is it wrong?

[long matrix]

cus u wrote it sotrue

the missing du's are a start

[neat lintel]

[neat lintel]

I keep doing $$\frac{d}{dy}$$ why am i like this

[fathom swallow]

Brandon H

[neat lintel]

Can you differentiate functions

say that $$f(x) = x^2+1$$

[fathom swallow]

Brandon H

[neat lintel]

can you do $$\frac{d}{df(x)} ln(x)$$

[fathom swallow]

Brandon H

[storm sage]

No

But if f is invertible, you can set (u = f(x)) and then do
[\frac{\dd}{\dd u}\ln(f^{-1}(u))]

[fathom swallow]

eulerEMILYteristic

[storm sage]

Which seems like the same thing as what you wanted?

[languid marten]

d(x^2+1) = 2xdx ?

[wet mortar]

ye

also dlog(x)=dx/x

[storm sage]

Using the chain rule I guess this is just the same thing as [\frac{\left(\frac{\dd}{\dd x}\ln(x)\right)}{\left(\frac{\dd f}{\dd x}\right)}]

[fathom swallow]

eulerEMILYteristic

[storm sage]

@neat lintel

[neat lintel]

I don't understand anything

[wet mortar]

so dlog(x)=1/2x^2 d(x^2+1)

[storm sage]

What part is hard to understand

[alpine kindle]

i hate this

[wet mortar]

away from 0

[long matrix]

0 = 0 guys, lets walk away

[alpine kindle]

are you sure shuri

[storm sage]

If there were something that this notation meant

[long matrix]

bruh this crap is just differentiation and integration, stop hacking

[storm sage]

It would be this

[neat lintel]

No, but...
what does setting u to f(x) do?

[storm sage]

I'm just giving f(x) a name

[wet mortar]

nah this

[long matrix]

yeah stop hacking

[storm sage]

And putting everything in terms of it

Which is possible if f is invertible

[neat lintel]

oh i see

its the exact same thing

[wet mortar]

ratiod by differential forms

[storm sage]

(which it isn't in this case, but whatever lol)

[long matrix]

no u

[storm sage]

that's called "de rham"

[neat lintel]

TY eric

[ripe dirge]

hmm

Variable separable

[solar hawk]

hello shuri

[long matrix]

if u ask the students who do this in integrals, how many can justify

[solar hawk]

why is \int dy = y bad??

[long matrix]

no thats perfectly sane. apart from the +C if its relevant

[solar hawk]

what no

[solar hawk]

i mean dy = f'(x)dx

\int f'(x)dx = \int dy = y = f(x) (all +C)

[long matrix]

well theyre not justified as fractions at that point

or whatever

differential forms things

[long matrix]

but this is what id be after

that's FTC

[solar hawk]

why but dy = ..dx is correct rigt

[long matrix]

FTC.

[solar hawk]

whot

[long matrix]

chain rule for integrals ig

fundamental thm of calculus

[solar hawk]

ok

[long matrix]

\int (dy/dx) dx = y + C = \int dy

is actually the order

then the 1st is ftc

ig the 2nd also is? been too long

[solar hawk]

idk

first ftc is they r oppposites

second is relate area to ROC

[wet mortar]

I don't remember what ftc is

[long matrix]

,,\int^x f(t) \dd t = F(x)

[long matrix]

There exists some antiderivative of f, F

that solves this

should be 1st FTC (under whatever conditions)

I... think.

And then all antiderivatives are a constant apart (given connected domain) should be a lemma or something?

[long matrix]

and that should net you both equalities I'd hope

[solar hawk]

what does the one bound mean?

ik if there is one bound on the bottom

its usually a set or domain or smthn

[long matrix]

another notation for improper integral

[honest breach]

yea

[solar hawk]

ah

[long matrix]

that I think i prefer

[solar hawk]

so

would

$\int^6 f(x)dx = F(6)$?

• C

[fathom swallow]

amukh1 | JS fanboy

[long matrix]

nah nah

[solar hawk]

aw

[long matrix]

that x has to be the variable

[long matrix]

this is like asking about dy/d6

that x at the top simply indicates it will be the variable of the antiderivative

[solar hawk]

i see

[solar hawk]

isnt that implied in the dx though?

[long matrix]

no check what i wrote

[solar hawk]

oh

[long matrix]

i differentiated between the dummy and free variable

[solar hawk]

ohh

yeah i do that with \int_0^x

[long matrix]

yh but like _0 isnt always a valid choice

[solar hawk]

which obv doesnt work that well

[long matrix]

thays very specific

[solar hawk]

but its okay for simple ones in desmos

[long matrix]

thats F(x) - F(0) which is a specific antiderivative

[long matrix]

which is fine for whatever u wanna do

but its definite.

[solar hawk]

yea ik

[long matrix]

But Im just thinking to myself if this could make sense, given u fix the constant of integration...

I dont think so atm.

like it doesnt really make sense to 'fix' that constant for an indefinite integral

[solar hawk]

yea it doesnt make sense in this way

[long matrix]

yeah so indefinite integrals r focusing on the functions themselves

rather than points theyre evaluated at

[solid snow]

I actually misread artanh as regular arctangent

What you wrote is correct apart from the dy typo

[zealous garden]

I still don't know what sinh and cosh are

[languid marten]

Are hyperbolic trig fn covered in a usual hs calc course ? Coz I didn't study this stuff at all in mine

[storm sage]

No

[storm sage]

Every function can be split into an even and an odd part

i.e. if you have f there are unique f_e and f_o such that f = f_e + f_o

And f_e is even and f_o is odd

Guess what cosh and sinh are the even and odd part of?

[burnt ledge]

sym and antisym slns to f"=f

[zealous garden]

e^x?

[wet mortar]

[faint garden]

Why does "e" keep showing up everywhere 😡

[modest rune]

you take the exponential formulas for sin and cos over C and get rid of the i

[solar hawk]

Wait I don’t know hyperbolic trig either I thought it is a precalc thing and it’s not ?

Is it a calc+ thing

[modest rune]

some college calc classes choose to cover it

others dont

it shows up in niche places so most people don't see it in highschool

[faint garden]

Wait a second. You know how the 2d trig functions use the unit circle? Do the 3d trig functions use the unit sphere because that would be super nice and intuitive.

[still latch]

The sphere is usually parametrized as follows:
\begin{equation*}\begin{split}
x &= r \sin(\theta) \cos(\varphi) \
y &= r \sin(\theta) \sin(\varphi) \
z &= r \cos(\theta) \
\end{split}\end{equation*}

[fathom swallow]

matrisemann

[still latch]

So there's no need for any new or fancy trig functions in this case

[storm sage]

yuparoo

[storm sage]

You learn it when you learn it

[solar hawk]

But I’m not supposed to know

It right

[storm sage]

Topics generally don't fit into class categories, and every class is different

Don't worry about it

[solar hawk]

Okay

[zealous garden]

That's cool and all, but what's the geometry

Like if I ask what cos and sin are, you and respond with the even and odd parts of the complex exponential, you aren't wrong exactly

[prisma plinth]

real geometry or complex geometry?

[zealous garden]

But you've enlightened me none

You've not shown me the circle for example

[modest rune]

i think those are very enlightening...

[zealous garden]

Unless you include your circle exposition in the complex exponential

[prisma plinth]

I think that the "area"->position correspondance between the hyperbolics and the sines and their corresponding conic hold for both

[zealous garden]

I think it's enlightening if you have background information that isn't right to take for granted

[prisma plinth]

Let me actually test something lmao

[modest rune]

...

[zealous garden]

The complex exponential example I mean

[prisma plinth]

I have a sort of geometric intuition

@zealous garden want a sort of geometric intution

[zealous garden]

Yes please

[languid marten]

is it like analogous to the unit circle geometric intreperetation of trig functions ?

[prisma plinth]

Let me draw out a desmos interpretation rq

https://www.desmos.com/calculator/mscaibvjbe

Just look at the picture

The hyperbolic argument is the unique argument such that, the area between the line to (cosh(phi),sinh(phi)) from the origin and the hyperbola going to the aforementioned point is half the argument

essentially it takes the angle, and finds the point with that area/2 in the sector

same thing works with the circular ones

replace hyperbola with circle

[storm sage]

Have you heard of a "hyperbola"

:p

[storm sage]

Yeah you are lol

Real and imaginary parts

[languid marten]

wait how'd you do the area thing with circles ? x tan(x) - sin(x)cos(x)/2 = x/2 ?

[storm sage]

the area of a sector of the unit circle is equal to the angle divided by two

[tepid light]

boom boom boom archimede's spiral

[zealous garden]

Lmfao

[zealous garden]

And that's why the area of a circle is τr^2/2

[zealous garden]

Yes, but I certainly did not understand the connection

[storm sage]

I see

cosh is the x part of the hyperbola

sinh is the y part

[burnt ledge]

what happens if instead of doing it based on the hyperbolic area you used the arc legtnh along the hyperbola

[storm sage]

No idea

It'd be a lot weirder

The functions would be bounded between -1 and 1

I feel like this isn't too hard to explicitly compute

[burnt ledge]

how would it be bounded between -1 and 1

[storm sage]

Because the x-coordinate is always less than the arc length

Oh wait

That made more sense in my head

Nvm

Lol

I was thinking of the ratios, but that's not how this works

[languid marten]

hmm if we define arc length equals argument /2 then we will get a different hyperbola ?

[burnt ledge]

https://cdn.discordapp.com/attachments/461293758361763865/1134654787565129849/Screenshot_2023-07-29-02-12-37-998_com.adsk.sketchbook-edit.jpg

Like this basically

what is the new "cosh" and "sinh" actaully

[languid marten]

ahh okay it seems like a reasonable way to define cosh and sinh i think

[burnt ledge]

like basically I've never understood why they actually use that area divided by 2

Like i get that its technically yhe same as putting circle area divided by 2

[languid marten]

yeah these two are equivalent

[burnt ledge]

but nobody ever really saya that thats just a fun tidbit surely

for circle everyone uses arc length

why to change their mind on the hyperbola

[languid marten]

hmm so the trig functions are defined in the arc length manner

arc length = rtheta = theta (r = 1)

[zealous garden]

Well the interesting thing

Is that the geometric product

I got nothing

[burnt ledge]

ahaha

[zealous garden]

It makes sense to me

I'm not sure how to articulate why

[prisma plinth]

Both are two sides of the same conic coin

[burnt ledge]

everything i know about geometric product comes from like three YouTube videos tbh

[zealous garden]

Okay, take a Euclidean (or Anti Euclidean) 2D space, then your bivector squares to -1 and your rotors look like complex numbers

[prisma plinth]

I used to be interested in geometric algebra, then I learned about abstract math and found that much structure scary :troll:

[zealous garden]

With definition of magnitude as sqrt(A A^\dagger) your (unit) rotors look like the unit circle in your spinor plane

However in a mixed signature space your bivector will square to 1 and I assume your unit rotors look like a hyperbola, and perform Lorentz boosts instead of Euclidean rotations

[burnt ledge]

yeag and rotors like split comlex right

[zealous garden]

Yes

[burnt ledge]

okayyy now what

[zealous garden]

The connection being the areas in the cosh sinh and cos sin thing

And Geometric algebra representing orthogonal transformations, ones that preserve area

[burnt ledge]

Ohhhh and their areas bc bivecotrs

[zealous garden]

Yes, that too

So it's like an equivalence between the hyperbola and circle

[burnt ledge]

roght at the start u said "or anti euclidean" what is that

[flat harbor]

theres also the connection where the "angle" is the arc length

[zealous garden]

Euclidean means unit e_i has norm 1, Anti means norm -1

[flat harbor]

i think this goes with this

[prisma plinth]

I thought the area * 2 = arc thing was only for the circle

[zealous garden]

So R^0,n

[prisma plinth]

idk if it held for the hyperbola too

[burnt ledge]

Ohhh right wraith i c

[burnt ledge]

i think the arc length varies w hyperbolic area in a weird way but i dont have any idea wjy i think that

[prisma plinth]

well arclength in the case of the circle is nice because it's integrating over essentially |dv|

which is tied to the circle

due to the absval

not sure if that's so nice for the hyperbolic one? idk

[flat harbor]

iirc its connected to the parameter that goes into the area

not the area itself

lemme check

[zealous garden]

Oh that's cool

So if I imagine the (double) cone and think of a plane slicing it

Nevermind I don't like it anymore

[flat harbor]

conics

[prisma plinth]

wait til you learn about projective geometry

then that cone slicing thing makes sense lol

[burnt ledge]

Now i gotta sleep but i will think more tmr

[prisma plinth]

not for a while tho :troll:

[zealous garden]

No cone slicing makes sense

[burnt ledge]

gns

[zealous garden]

But the idea didn't line up like I thought

[zealous garden]

Gn harper

Little homie

[flat harbor]

sweet dreems

[zealous garden]

What's a 4-cone

[prisma plinth]

wh at

[zealous garden]

The object that looks like a linear interpolation of a sphere to a point over some separation in a 4th spatial dimension

What's the proper name

[prisma plinth]

idk what you're talking about

sounds like a Stareographic projection idk

[zealous garden]

So like

A 1-cone is a line segment

A 2-cone is a triangle

A 3-cone is a cone

A 4-cone is ???

Do you see the pattern

An N cone is a (n-1) sphere scaled down to a point over some distance

[prisma plinth]

sounds like the zero set of some quadratic homogeneous poly

[zealous garden]

Probably is

In fact I bet it's the "unit circle" of spacetime

Or something close to it

[prisma plinth]

I thought spacetime uses the quadratic form x^2 + y^2 + z^2 - t^2

which is homogenous

[zealous garden]

Or t^2 - x^2 - y^2 - z^2

[prisma plinth]

idk maybe

I never understood that

[zealous garden]

Mostly minuses

[prisma plinth]

I only know it from constructions of integral quadratic modules

[zealous garden]

What

[prisma plinth]

Refer to Serre's "A Course In Arithmetic"

[zealous garden]

Anyways we need to know which one is the truth

Because R^1,3 and R^3,1 don't have the same symmetries

[prisma plinth]

It's mostly a model of spacetime afaik

[zealous garden]

They have the same spin groups, which it turns out is where all of our observables seem to come from, so there's no easy way to see which we're in

Assuming that the model is an accurate enough one for us to be "in" either one

[zealous garden]

Yes

The question is whether time squares negative and everything else positive, or if time squares positive and everything else negative

The latter is associated with the quaternions for obvious reasons

It was also chosen to be the metric for the standard treatment of SpaceTime Algebra

G^1,3, which is algebra isomorphic to G^4 (which could be posed as a model of spacetime where all directions square to 1)

That said, the other choice, G^3,1, is not algebra isomorphic to either of them

[storm sage]

A cone over X is the topological space X×[0,1] / X×{0}

i.e. it's a cylinder over X and then you squish the top side to a point

[zealous garden]

Yeah sure that's one way to say it

But what's the name of the 4 dimensional example

The example just beyond human geometry

[storm sage]

topologically it's just a 4-ball

I dunno if the specific shape embedded in R^4 has a name though

[zealous garden]

Lmfao

asks question about the name of the 2 dimensional shape with 2 pairs of parallel sides
idk but it's topologically a circle

I do love this

[zealous garden]

It is now the glone

[storm sage]

It's just true

:p

[zealous garden]

Waiting for the introductory Geometric Calculus text with an exercise involving integrating a multivector field over the surface of a Glone

With my name on it

15 years, just you wait

[storm sage]

Write it

Go

[zealous garden]

[upper shuttle]

marry me

[mental stratus]

[ripe dirge]

[serene pulsar]

I don't have to study until school starts but I also don't know what to do now that I'm not studying math. I certainly need a break but my brain can only think of doing more math at this point lol.

I might do the Khan academy calculus while waiting for school to start.

But I also feel like I should play some videogames to rejuvenate.

I kind of want to go back to playing Shenzhen I/O, I love that game.

Even if I only play the solitaire part

[flat harbor]

shenzhen!!! woooo!!!!

[serene pulsar]

It's so fun, but I have a habit of binging a game and then stopping halfway through. Last thing I was doing was making Tetris for the "make a game" level.

But I got annoyed because even though I put the Tetris music in, it wasn't compatible with the other embedded devices sleep times. I struggle a lot with the sleep times.

[rocky shuttle]

zachtronics

[junior jolt]

guys

what does ai research look like?

is it legit just

come up with a bunch of architectures and try them out

[river moon]

https://arxiv.org/pdf/1910.03867.pdf

[uneven pond]

I know that a lot of people (including me partially) don't believe the alien stuff in the news, but if it was real, do you think the only reason we got to the moon was because of alien tech, because the first "ufo crash" was in Roswell in the 1940s

[proven plinth]

Do you really think that the technology we "derived" from a vessel that is most likely capable of flying several light years is in form of a saturn v

[uneven pond]

idk im kinda just spitballing theories lol

i dont really believe its real

but its a cool concept to think about

[mental stratus]

the universe is a smooth manifold?

[languid marten]

locally homeomorphic to R^3

Ahh wait smooth means differetiable ?

[loud snow]

Aliens are real but we haven’t seen any obvious or intentional signs of them is my opinion.

[west mauve]

you believe in it too 😮

[frank lantern]

My opinion is that there is a very high probability that aliens are real, but I'm not completely sure.

[gaunt quest]

I mean the universe is very big so I guess it's reasonable to think there are aliens somewhere

but that size also works against us ever interacting with them

[loud snow]

Its one of those things that is very likely and we are far from conclusive proof. General consensus should be that they exist by all accounts of human intution about expansiveness of space

[frank lantern]

True. Even if the aliens aren't technologically advanced enough to explore space, it's still much more likely for primitive organisms like unicellular ones to exist in some planet out there.

[gaunt quest]

I'd go so far as to say that the size makes exploring space unreasonably difficult. it isn't just about the tech needed to accelerate in reasonable time to near light speeds, but also the fact that travelling at them is incredibly difficult

there are lots of things in space and such fast speeds make really high energy collisions even with tiny masses

the whole E = mv^2 relation

I think any alien capable of moving outside their planet is constrained pretty badly by this, so we'd only get to explore small neighborhoods near us. something like radio signals is more likely ig

[faint garden]

Even if aliens existed it would probably just be some stupid dog like thing.

[burnt ledge]

@junior jolt, show this person the truth

[junior jolt]

nah because we use rockets

they just fly around with no propulsion

[burnt ledge]

Same with pirates

for our human ships we use diesel and fuel oil engines

but pirate ships have no engines they just sail with no propulsion

[junior jolt]

💀

Maybe pirates are real

[faint garden]

I'm not a pirate. I definitely pay for all my books 👀

[ripe dirge]

I can't pay for books so I source it via piracy

Sadly

Need second hand copies of the book in hard copy one day

[storm sage]

Hey everyone, Discord will shut us down if we allow conversations about piracy on this server, so imma ask you all to please not talk about it unfortunately

[ripe dirge]

Okay

Cheese

[storm sage]

Brie

[ripe dirge]

Toblerone

[rocky shuttle]

Taco

[tame egret]

burger

[rocky shuttle]

Cat

[tame egret]

dog

[rocky shuttle]

Goat

[tame egret]

sheep

[rocky shuttle]

Cheese

[ripe dirge]

milk

[rocky shuttle]

Pizza

[tame egret]

yoghurt

[rocky shuttle]

Gorilla

[tame egret]

ice cream

[rocky shuttle]

Groundhog

[tame egret]

spider monkey

[rocky shuttle]

Narwhal

[tame egret]

ant eater

[tame egret]

orca

[ripe dirge]

Bird is the word

[ripe dirge]

cringe

[tame egret]

lol

[junior jolt]

🤓

[mental stratus]

the multinomial theorem will be the end of me

[burnt ledge]

See the server and also discord are in cahoots to stop us from talking about the truth behind pirates. Believe me yet ?

[junior jolt]

Yes

Seems like a coverup

[prisma plinth]

why lol

[neat lintel]

i hope not

[tame egret]

no.

[burnt dune]

yo guys

let I be an ideal

I^n would be the set of all x such that x is a sum of elements in I right?

now suppose we are over a noetherian ring\

[mental stratus]

why not

[burnt dune]

then I^n would be finitely generated

or no

I would be finitely generated

so that I^n would be the set of all sums of just the generators

or better it would be a polynomial over those

is that correct?

so that I^n would be a set of polynomials over the generators?

[prisma plinth]

iff I is principle

[loud snow]

Its a power of ideal so its n’th powers of generators of I

[prisma plinth]

Which R[X] is a principle ideal domain iff R is a field, i.e R has no nontrivial ideals beyond (0)

[velvet dagger]

What

Take any non-principal ideal in a Noetherian ring

Instant counterexample

[prisma plinth]

I had a brain fart of biblical proportions

I misread the problem massively

[prisma plinth]

ALL ideals in a noetherian ring are finitely generated

[burnt dune]

ik

thats what i meant

its for a proof of krull intersection theorem

ty hto

tho*

[prisma plinth]

Well

Take an ideal I, and say it has finitely many generators (in the ring sense), denote them x_1…x_N

*big thinking*

so the valuation map from the polynomial ring R[X_1…X_N] to R rhat sends X_n to x_n should have an image that contains I?

i need to think about this a bit more, i know that isn’t right

NO, WAIT

CORRECTION:

the image of the ideal (X_1…X_N) will be that finitely generated ideal

i.e kernel of the map that sends all the vars to 0

i just forgot about the constant coeffs lol

[neat lintel]

[storm sage]

Yeah seems legit

[prisma plinth]

the image of the ideal is an ideal cuz any poly map into it’s base ring is surjective

that’s a valution map

[storm sage]

(Doesn't know what a valuation map is) Nods

[prisma plinth]

Map from R[X] to R that fixes R

valuation as in, gives X a value

if you wish, associative R alg morphism

[storm sage]

Oh I think that's called an evaluation map

[prisma plinth]

oh that gives me an absolutely vile statement of R[X] being noetherian

[prisma plinth]

okay got it

[storm sage]

My understanding of a valuation is that it's like an absolute value on a field

[prisma plinth]

Oh yeah

[storm sage]

But I know nothing!

[prisma plinth]

If R is noetherian, then forall ideals I, I is the image of the ideal (X_1…X_N) in R[X_1…X_N] for some N under some epimorphism that fixes R

absolutely abomidable

[storm sage]

?

Isn't that by definition

Although I'm not sure how "epimorphism" comes into it

[prisma plinth]

so that image of ideal is necessarily ideal

[proven plinth]

taking the derivative of quadra composite functions is so confusing

[cold rivet]

khan academy has a list of courses

and its in the order you should take them in

its only on mobile tho

oh damn it

i cant share a picture

it was a really funny set up to the joke

(╯°□°)╯︵ ┻━┻

[prisma plinth]

wow. That was about as well done as tartare

[serene pulsar]

It's on desktop too

[flint basin]

Chain rule goes brrrr

[jagged forge]

oh is that what they meant by quadra composite

[flint basin]

I imagine

[mental stratus]

imagine all the people

[rocky shuttle]

imagi nation

[sonic sentinel]

there was one text message on whatsapp computer that was typed in reverse until i clicked on it

then it turned back to normal

it seems like such a burlesque(right word?) glitch

like the whole letters and everything were in reverse

[red rune]

would a B in abstract algebra look bad on a transfer transcript?

[storm sage]

I mean it would look better than a C but worse than an A

I dunno how much else we can say without more context

[red rune]

whats average usually for abstract?

in my class, most got Cs or Fs and no one got an A

[tall girder]

Hello

Hello?

[red rune]

hi

[tall girder]

i have a question

[red rune]

yes

[tall girder]

If 0 degrees C = 32 degrees F, does that mean that 0 degrees C + 0 degrees C = 64 degrees F

?

[red rune]

thats exactly correct

[tall girder]

YES!!!

THANK YOU!

[flint basin]

No one at all? Out of how many people?

[red rune]

like 15. on one test, the average was ~50 with a high of 73

[flint basin]

Well if averages go on your transcript (not every place does this), that'd probably be fine?

If not and your other grades are good, then also probably fine?

[tall girder]

sorry, just a question out of random, do you play soccer?

[storm sage]

Also I think this just depends on the prof

Every class will be different

[red rune]

do schools care more about classes that are related to major when transferring? Like if im transferring to CS, would they even care that much compared to just calculus and such?

[tall girder]

ok

Bye

[storm sage]

Probably yes schools care more about the in-major classes

[mint patio]

Can you induce long-term cyanide poisoning if you eat enough apple seeds?

Idk how chemistry works

[solar hawk]

probably

me neither

[mint patio]

I’ve just heard you can accidentally do it

[solar hawk]

lmao your profile 💀

[mint patio]

What about it? 😛

[solar hawk]

idk

lmao the pronouns section is the funniest part

[mint patio]

🤣

That’s the intent

[solar hawk]

especially since they are in your bio when there is a dedicated section 😭

[mint patio]

Well see

I don’t rlly care abt my pronouns

but I do care abt being submissive and breedable

[solar hawk]

damn

[mint patio]

gotta let the manipulative epeople know they can take advantage of me ya feel

[solar hawk]

i mean yea that does make sense

[mint patio]

LMFAOOOOOO DOES IT??

[solar hawk]

;-;

[solar hawk]

IDK

I WAS JUST AGREEING ;-;

[mint patio]

ikik it’s cute dw 🤣 I’m glad you like it

[solar hawk]

okay

cool

[faint garden]

👀

[flint basin]

👀

[solar hawk]

👀

[mint patio]

[solar hawk]

literally the perfect emoji for that moment.

[latent edge]

breedable hmm sounds legit

[celest bay]

Pythragoras theoreom help me

Pls

Im struggling learning it

[ripe dirge]

[solar hawk]

username includes "the sigma"
guys help i struggling Pythragoras "theoreom"

[jagged forge]

only a true sigma is willing to ask for help when he needs it

he doesn’t concern himself with the beta male’s opinion of him

[neat lintel]

it is only when a mosquito lands on one's balls that man realizes not to use violence

[jagged forge]

what a delicate analogy

just like one’s balls

[solar hawk]

Lmao

[faint garden]

The pythagorean theorm isn't intutive at all tbh. Like algebraically I see how it works but my intuition doesn't really understand or believe it.

Like the fact that x^2+y^2=1 makes a circle is so jank

I would have thought |x|+|y|=1 would make a circle

[solar hawk]

No

Look at a proof of the Pythagorean theorem

[solar hawk]

The circle is the collection of points with equal DISTANCE

Distance brings in the pythag theo

[faint garden]

Idk the fact that walking diagonally is faster than walking horizontally and then vertically is so weird.

[fringe needle]

This is more the triangle inequality than Pythagoras

[steel pelican]

hi everyone i am new to this server and i am in year 7 and might need some help

[fringe needle]

I would argue the triangle inequality is very intuitive

Pythagoras I have to agree feels unintuitive at a first look

There’s no clear reason at first why side lengths should be related by a weird sum of squares relation

[jagged forge]

Isn’t this slightly backwards, isn’t the distance formula more a consequence of the Pythagorean identity

[faint garden]

When I found out about pythagoras I measured a bunch of triangles with a ruler because I didn't believe it 💀

[fringe needle]

You can’t expect |x| + |y| = 1 to give a circle though simply because it’s a collection of linear relations

[solar hawk]

well i mean

[fringe needle]

It is a pretty crazy theorem imo, surprisingly underrated

[solar hawk]

i dont care abt distance formula

[fringe needle]

Even if proving it is easy

[solar hawk]

the pythagorean theorem has always been the pythagoran theorem

[steel pelican]

12 x 3 + 5 x 2 + 4 x - 6 for x = -1 how do you solve this

[solar hawk]

i didnt fall for that distance formula bullshit

[jagged forge]

but the set of equidistant points is only a circle if you use the usual Euclidean distance

[steel pelican]

i am confused

[solar hawk]

waever

stop overcomplic

oke

circle = set of points with equal distance

pythagoran theorem gives distance between some points

[fringe needle]

The point is it isn’t necessarily intuitive how to compute distance if one doesn’t find the Pythagorean theorem intuitive

[solar hawk]

right

i get it

which is why

[fringe needle]

Im willing to say that I’ve just been black boxing Pythagoras my whole life

[solar hawk]

i told him to go look at the proof

go look at the proof
[explanation of circle]

[fringe needle]

Understanding a proof is not the same as feeling like you understand the reasons for the result

I don’t think it’s a bad thing

[solar hawk]

yea idk i cant help with that

[solar hawk]

yo open a help channel wait 15 mins and ping helpers

i dont get paid enough for this

[fringe needle]

I think it’s fundamental enough that it’s one of those things that should serve as building intuition rather than being intuited

[solar hawk]

(i get paid $0)

[faint garden]

If you think of the x and y axis as two infinitely long rulers then distance on the coordinate plane starts to look kind of weird

[steel pelican]

i need help

with

12 x 3 + 5 x 2 + 4 x - 6 for x = -1

[solar hawk]

infinite..?

[jagged forge]

if you can’t help with that don’t dismiss it, just don’t say anything

otherwise you’re not being helpful

[faint garden]

Yeah because the x and y axis extend infinitely

[solar hawk]

open 👏 a 👏 help 👏 channel

!help

[quasi jetty]

Please read #❓how-to-get-help

[steel pelican]

i am new i dont know

[solar hawk]

well i tried

[fringe needle]

Then read the channel that was linked

There are explanations there

[solar hawk]

but then people kept correcting random shit

the distance formula is literally just the applied pythagoran theorem

its not the pythagorean theorem + anything its literally just the pythagorean theorem

[fringe needle]

As far as I understood the convo no one was doubting this

[faint garden]

The distance formula is kind of lame. Like it's something that you should be able to instantly rederive if you understand the 2d cartesian plane. You don't really need a formula for it.

[solar hawk]

yea anyway the circle equation isnt x + y = 1, because that is the set of points whos sum is 1

[faint garden]

Well |x|+|y|=1 is a circle in taxicab distance

[fringe needle]

Not the point

[jagged forge]

well, it’s not a circle

but it is a set of equidistant points using the taxicab distance

[fringe needle]

In some texts it would be called the unit circle for that metric

But that’s beyond the point anyways

[jagged forge]

perhaps

[long matrix]

defn of circle to me

[long matrix]

A (euclidean) circle is invariant under change of orthonormal basis, but we want the formula under some choice of x, y.
The formula at least has to be somehow invariant under chance of orthonormal basis

and well |x|+|y| = 1 doesnt cut it.

I'm sure there's more into it if you look for the why

[river moon]

square is a circle, line segment is a circle

[rocky shuttle]

how is a line segment a circle

[long matrix]

<@&268886789983436800>

[leaden torrent]

yeah please dont

mute lasts 10 mins

[cold rivet]

I was recently told calculus BC

is calc 1 and calc 2

and calculus AB was just calc 1

i though AB was just the first semester of calc 1 and it was a year course

someone explain

[storm sage]

the names for classes are pretty arbitrary

But AB calculus generally covers a first semester in calculus and the parts of BC calculus which aren't covered in AB are generally a second semester in calculus

[cold rivet]

they are arbritray but standard

no?

[storm sage]

Well

There are college board curricula for AB and BC calculus, but classes usually don't exclusively cover those topics

And calculus 1 and 2 aren't standardized

[faint garden]

We need a dishonorable role

[rocky shuttle]

— role

[zealous garden]

It's me, wraithlord_koto, continuing the campaign for cohonorable

[storm sage]

hmmmm

@zealous garden

[burnt ledge]

wraithlord cohonorable

[jagged forge]

euleremily is suppressing the cohonorable campaign. i wont stand for this injustice

[storm sage]

I thought this is what they wanted, cohonorable?

[solar hawk]

whats cohonorable

[jagged forge]

dual object of honorable in the category of roles

[zealous garden]

LMFAO

[latent edge]

best role

[zealous garden]

A great example of cohonorable is Wew

[storm sage]

Hmmm hold your horses on that one

[mental stratus]

no

[fringe summit]

Or me

[mental stratus]

co honourable means complement is honourable?

[storm sage]

Honorable means they're a role model to the server

Cohonorable means the server is a role model to them

[tight comet]

[mental stratus]

Tension

[zealous garden]

Well if that's what cohonorable means

I don't want it anymore

New campaign

Kohonorable

[static loom]

i want cohonorable

[zealous garden]

Lmfao

[static loom]

bow before me!!

[zealous garden]

If you're both honorable and cohonorable, can you get bihonorable

[storm sage]

You can get bifurious

[zealous garden]

Lmfao

Can I get autohonorable, I'm a role model to myself

[static loom]

to get autohomorable you must be fully faithful

[mental stratus]

endohonorable

homorable

[faint garden]

I think that fundementally we just need a role that will shame people and make them feel bad

[neat lintel]

that's the gamma role

[zealous garden]

Thank you for your service

[mint patio]

Oh

LMAO

So I’m guessing bad math memes don’t count

[neat lintel]

I am missing my honorable role

[eager reef]

Where did it go

[velvet dagger]

Okay so

[wet mortar]

https://m.youtube.com/watch?v=8Gs6pFM-B5I

[velvet dagger]

Posting here since math discussion is nominally for math

https://youtu.be/mcExlu3NQaY

[mint patio]

Yep I have this one

[wet mortar]

tevvez goes hard in general

[mint patio]

I like Colin Hennerz a lot but idk if I’d classify as hardstyle

https://youtube.com/watch?v=yEN8CxxBW7w

[fringe summit]

Questionable title

[mint patio]

https://youtube.com/watch?v=FxLCtEw5iVg

[wet mortar]

oh I know one that's similar

[mint patio]

Every League player knows this one

https://youtube.com/watch?v=nUqwXoaSHK4

[wet mortar]

https://m.youtube.com/watch?v=Wr225gT0yWI

[mint patio]

keep linking I’ll put it on my q for when I get back home

[jagged forge]

this is what I listen to

https://youtu.be/XnRRZb4C8WQ

[fringe summit]

https://youtu.be/CRbBFKZymN0

Hopping on the bandwagon

[jagged forge]

I saw appassionata and got excited and then I realized it says appassionato

[fringe summit]

Listen anyway

[jagged forge]

yeah it’s pretty

[deep mango]

rachmaninoff 🤢

listening to this right now

https://www.youtube.com/watch?v=HiQ94ht3QEw

chill portugese guitar

[jagged forge]

ooh this vibe

reminds me distantly of some parts from the song i posted

[deep mango]

idk what it is it just autoplayed after the last thing i listened to

that was this which was great

https://www.youtube.com/watch?v=qn-JPayT0Es

this is super good and fun, listened to it earlier

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

[jagged forge]

i may check out more of this Portuguese guitar

[fringe summit]

Classical era bad

[jagged forge]

cringe opinion

[deep mango]

late romantic / impressionist are best

but im not about rach

too maximalist

[fringe summit]

Not too big on Debussy

[deep mango]

fuuuuuuuuck you

ravel >>>>>> everyone, debussy second, chopin third

then beethoven because lets be honest he's a romantic composer

that's not some mozart trash

then jump up to satie, back to liszt, tchaikovsky, and maybe you start to near rachmaninoff

sibelius has to come first ofc

no one's as bad as haydn though (canonical worst famous composer)

[neat lintel]

shutup nerd

[fringe summit]

Based and true

[fringe summit]

Ravel cracked in orchestration

[jagged forge]

beethoven actually cared about form and coherence tho

but i agree on ravel and debussy

[deep mango]

sorry we can go back to discussing hatsune miku vocaloid

[deep mango]

and it held him back... so sad

[storm sage]

https://www.youtube.com/watch?v=tR7G0FNFDgQ

[storm sage]

Mozart though

[fringe summit]

L

[storm sage]

Oh shoot ryc and I agree on something

Need to change my opinion

Rachmaninoff is the BEST

[fringe summit]

Based

[storm sage]

Every Rachmaninoff link gets a Medtner reply

[deep mango]

is the shining example of why classical period music is horrid

[storm sage]

You're just like... wrong

The requiem is beautiful

The piano sonatas are also delights

[deep mango]

all of mozarts music is like "boopadoopadoo, doo doo diddly doo"

[storm sage]

The d minor concerto

Mozart is so emotional

Haydn also slaps af

[fringe summit]

https://youtu.be/esXUW0fInKE

[deep mango]

mozarts emotional in the way that a marvel fan gets emotional when their favorite superhero shows up in the new extended universe movie

[deep mango]

AAAAAAAAA

[storm sage]

You're just... wrong?

The Haydn fifths string quartet is one of the best ever written

I'll stand by that

[fringe summit]

https://soundcloud.com/alexheppelmann/moro-lasso

[storm sage]

And the jupiter symphony is genius

[deep mango]

has haydn ever written something that isn't sickeningly pastoral

[fringe summit]

This is a very changed arrangement of Gesualdo

[deep mango]

jupiter symphony is like the only bearable mozart piece

and it's not even the best orchestral piece called "jupiter"

im sorry maybe i like

saw the little einsteins movie too many times as a kid

and am just jaded on mozart

[storm sage]

tf

pastoral?

Not how I would describe the fifths string quartet

[deep mango]

i dont know what that is

im sure he can manage to make it as such

[storm sage]

Don't say you like Holst

[deep mango]

of course i do

but tbh the only planets i like are mars and jupiter

the others are gimmicky

[deep mango]

ok this is just a slightly sadder merry hunting troupe traipsing through a meadow

also i didnt put bach on my list but bach is obviously great

sort of outside all the other composers in my estimation though, satisfies a different need

[storm sage]

tf

Also @fringe summit do you know ludus tonalis

I think you would love it

[fringe summit]

https://soundcloud.com/phil-best/mendelssohn-venetian-gondola-song-op-30-no-6

Mendelssohn is good

[storm sage]

yesssss

I played the op 10b one

[deep mango]

mendelssohn is good, yes

i dont really know much of his work

[storm sage]

mendelssohn is the mozart of the romantic era

how can you like him but not mozart

like omg his midsummer night's dream overture screams mozart

it's beautiful

[jagged forge]

I can’t really even describe Mozart, other than, his concertos for me are like a perfect short story from beginning to end that never quite manages to be predictable but lands the ending in the most perfect and satisfying way possible

sonata form is just chefs kiss

[storm sage]

don giovanni has got to be one of my favorite operas

[jagged forge]

oh the ending of that is incredible

[storm sage]

it's filled to the brim with perfection

[jagged forge]

mozart can be dark when he wants to

but also tender and gentle

[storm sage]

wait isn't the ending just the rest of the characters cheering that the sinner has gone to hell lol

[jagged forge]

well I meant the song before that when don giovanni gets dragged to hell

[storm sage]

ohhh

yes that one is amazing

DON GIOVANNI

M'INVITASTE

[jagged forge]

my favorite performance of that is the one with Kurt Moll as the commendatore

Basso profondo

[storm sage]

I'll look it up!

[jagged forge]

apparently he sang the low A an octave down for fun one time and the director told him not to do that lol

[deep mango]

because i do not like classical era tropes and i do like romantic era tropes

i did see marriage of figaro and it was a lot of fun

[fringe summit]

I simply dislike classical period

[storm sage]

LOL

[jagged forge]

did you listen to him sing yet?

[static loom]

I like some music, but I hate instruments

[jagged forge]

like, acoustic instruments?

[static loom]

by acoustic do you mean just the ones that make sound?

[jagged forge]

no, like acoustic vs electric

[static loom]

ah

[jagged forge]

I’m just trying to pin down what u mean cuz I’m not sure what music isn’t produced by instruments

[static loom]

yeah

that confused me too, I thought you were asking if I just didn't like audible instruments

[jagged forge]

so what do you mean you hate instruments?

[static loom]

like the devices that make noise

[jagged forge]

im still confused lol. what kind of music do you like?

[static loom]

https://www.youtube.com/watch?v=AWVUp12XPpU

[jagged forge]

god dammit lol shoulda seen that coming

[static loom]

https://tenor.com/view/we-do-a-little-trolling-hamster-we-little-trolling-gif-21030970

[tepid light]

y his hands

goin like

🖐️

[solar hawk]

Mouth

[solar hawk]

Wow that’s a big elp

[jagged forge]

the voice is absolutely an instrument, and u are speaking to someone who majored in vocal performance in college lol

[solar hawk]

Lol

I never figured out the thing 😭

[pulsar fractal]

,av girid

Bug maybe

[fathom swallow]

User cancelled member selection.

Jul 31, 2023, 11:51 AM

[storm sage]

this is so gooddddd

[hoary isle]

does anyone know if there are any other math servers as big as this one?

[burnt ledge]

Yes i know that there isnt

[gaunt quest]

proof?

[burnt ledge]

No, knowledge

[gaunt quest]

knowledge without proof

[burnt ledge]

Yep

extremeley common

[gaunt quest]

depends on your idea of knowledge ig

[neat lintel]

can somebody guide me
i get stuck doing questions
ughh

[gaunt quest]

as a mathematician I refuse to accept anything without proof :)

[neat lintel]

mr blue i posted #help-3 here an example

[burnt ledge]

Have you eaten anything today

[gaunt quest]

yes

[burnt ledge]

Would you answer without knowing

and if not, can you prove you ate something today

[gaunt quest]

yes

[gaunt quest]

ofc there's remnants of the food I ate

[burnt ledge]

thats not a proof, those could be remnants of somethignelse

[gaunt quest]

then I'll shit the food out

show you the shit as proof

[burnt ledge]

Could have eaten thag yesterday, or might not be food, or any number of things

still isnt proof

Yet you still know these things

point is, either ur standard for proof is incredibly low, or you accept you know thjngs without proof

[torpid frost]

anyone got some combi qs?

[analog hedge]

guys!!!

i need help in a sets problem quick

To each element of the set S={1, 2, …., 1000} a colour is assigned. Suppose that for any two elements a, b of S, if 15 divides (a+b)then they are both assigned the same colour. What is the maximum possible number of distinct colours used?

#help-1

☝️ ☝️

[gaunt quest]

alternative 3rd interpretation, I just don't consider these things knowledge

[burnt ledge]

Thats fake as hell

[gaunt quest]

I treat all statements made in language to be probabilistic

[burnt ledge]

Lmao

Or maybe you dont, i guess

[gaunt quest]

and only consider statements proven directly from assumed axioms to be able to be knowledge

since then the probability of 1 carries forward from the axioms

[burnt ledge]

You just dont do that though, tbvh

[gaunt quest]

I think most people treat the word knowledge colloquially

but having knowledge of things at all is a very shaky concept to me

what are those paradoxes called

[zealous garden]

Knowledge is (a record of) experience or events

[burnt ledge]

idk itd have "epistemological" in there somewhere probably

[gaunt quest]

gettier problems iirc

since knowledge is often considered justified true belief, but you can end up in a situation where you justify your knowledge off incorrect information, but you turn out to be right

it's pure chance that you did, so it's not like you actually knew that

[zealous garden]

These things derived from axioms I wouldn't call knowledge

Knowing them, sure

There is a lot of knowledge in their expression or derivation

But knowledge to me is directly linked to experiences rather than any certainty of a reality or truth

[burnt ledge]

Oh i heardnof thise i think but idk what theur deal is. But i dont think tj matters because we all know (lol) what knowledge is, even if we cant define it in this or that way

[burnt ledge]

Yeag i agree

[gaunt quest]

haha I like that view

but I think it does matter to know what knowledge is, since otherwise the line between knowledge and just belief is fuzzy and doesn't describe that same thing

like I know qualitatively that there's a difference between things we know and things we believe

but without defining it then anyone could claim science is just belief and that feels wrong

[burnt ledge]

Yeag im saying we do already know what knowledge is and yhat the line btwn belief and knowledge ks already nkt blurry, rven if its hard to put words to the line

typos*

[gaunt quest]

I think without a definition it's blurry

[zealous garden]

Knowledge is something that exists within observers and agents

[gaunt quest]

knowledge without truth is kinda stinky though :/

[zealous garden]

I have the knowledge of what blue looks like to me

[gaunt quest]

not a useful idea to me

[burnt ledge]

i know what a house is, but i coildnt say for certain what a house is

[zealous garden]

There is no false knowledge

You can have knowledge that does not represent reality

But it is a true record of experience

[gaunt quest]

reality and truth wouldn't be the same to me, I would consider mathematical statements true but not real

[zealous garden]

If I am hallucinating I will have knowledge of things not reflected in reality

If I am delusional I will have knowledge of things that aren't true

You have knowledge of your dreams

Some of them at least

[gaunt quest]

on this point like, there could be something that looks a hell of a lot like a house but turns out to not be a living space. it reminds me of a model where you define negatively. when I don't know something the space of things it could be is infinite, but I learn what something isn't, and the remaining space of things is what I define that thing to be