serious-discussion

[light gate]

is eng even better paying than math

[stark hill]

Are there some engineering students here

[steep mountain]

Keep it in english please, and dont spam into other channels.

[dawn mist]

Can I ask you guys a physics question? If an electron is placed in a magnetic field directed towards Z+, will the electron move clockwise or counterclockwise??

I'm like 99% sure it moves clockwise but the answer key for my book says otherwise

Damn I'm stupid as fuck

[sharp mulch]

discord.gg/physics

[restive mirage]

That is haryanvi rap song

"A Russian gun in my hand, cloth tied on my face, girl.
When I shoot, I never miss the target, girl.
A golden strap hanging on my left side.
I keep finding excuses to take down enemies, girl.

Reckless boys with cloth tied over their faces, girl.
When we aim, we never miss the target, girl.
A golden strap hanging on the left side.
Always looking for chances to hit the goal and defeat rivals, girl."

[keen nimbus]

Is there one for biologists

[sharp mulch]

See #old-network

[steep mountain]

good to know twin, but thats irrelevant to what i said.

[restive mirage]

Who twin?

[steep mountain]

another term for friend

[restive mirage]

Hm.

[patent gorge]

GUYS! is wolfram is worth using.

?

[unborn meteor]

not for cheating

for general use yes

[patent gorge]

uhm

but its paid vro

[unborn meteor]

its free if you don't want steps

the other day i spent an hour trying to do an integral

[patent gorge]

and takes up a lot of space in desk!

[unborn meteor]

i eventually gave up and put it into wolfram

[patent gorge]

cheater

[unborn meteor]

i mean it wasn't for class it was a personal project

so not cheating

[patent gorge]

is that was your homework or were u just doing anything on that day?

ojh

got it

[unborn meteor]

yeah not for school

so its allowed

[patent gorge]

btw how to download it?

[unborn meteor]

just google wolfram alpha

its a website

[patent gorge]

any link or website?

okay

[unborn meteor]

but please please please

don't use it to cheat

if you want help you can open a help thing here, see #❓how-to-get-help

[patent gorge]

but i asked to LLM(GPT budddy) ,and he gave me list of bunch wolfram(s)!

[patent gorge]

why r u saying this?

mmmm..

[unborn meteor]

because cheating is bad

you don't learn

also you could get in really big trouble

[patent gorge]

did u ever do that
?

hmmmmmm

[unborn meteor]

i've never cheated

that i know of

[patent gorge]

What u r studying bro(currently!)

Im learning determinats now!

before*

[unborn meteor]

uhhh

calculus

at least in school i'm doing calculus

[patent gorge]

in which grad u r ?

sophomore?

or Senior?

[unborn meteor]

high school

[patent gorge]

india?

[unborn meteor]

10th grade in the USA

[patent gorge]

wow

[unborn meteor]

the grades are different around the world

[patent gorge]

in 10th grade , you r learning calculus? i mean at age 15 (or less)?

[unborn meteor]

age 16

[patent gorge]

is it much common there (in USA)?

[unborn meteor]

idk

[patent gorge]

in India and in other-most countries ,I had heard that ,kids usually learn Calculus and even Linear algerba(bruttaly partially) in their grade 11th, but still at that lvl most students didnt learn them properly ,only drills and rote memorization, no any deep on "WHY"!

how unlucky

[zinc talon]

bruh what

[patent gorge]

but still ,somone curious like einstein can study before grade 11

[patent gorge]

why r u frying vro?

[zinc talon]

bro

[patent gorge]

yes?

[zinc talon]

bruh even in india you aint gonna be good at calc without the deeper understanding part

[weary arrow]

Hey guys, I've got a question regarding momentum flow, if I've got a mass on a jumping frame which has no mass, then will there be any flow in a corner which is not required for the flow to go through to get to the ground? No right

[patent gorge]

but its all formula based

[zinc talon]

what is

dude

😭🙏

[unborn meteor]

wow

[zinc talon]

just name some formulas that they dont teach in america

or smth essential without which you cnat solve questions

[patent gorge]

so you r probably saying ,they teach and derve all formulas with proofs on calculus , R u sure?

[zinc talon]

yeh

im indian

in 11th

[patent gorge]

anyways ,R u indian?

[patent gorge]

Where?

i never see it on yotube

[zinc talon]

ncr

[patent gorge]

at all

[patent gorge]

wdym

[zinc talon]

i thoght you were asking fro region

[zinc talon]

coachings?

[patent gorge]

Anyways R u indian?

[zinc talon]

its there bruv

[zinc talon]

yes

i already said yes

[patent gorge]

which channel?dm me and send me link or send me here

[zinc talon]

bro just search on yt

for xyz topic

derivation

its all there

hindi

and english

[patent gorge]

SO most probably which channel?

[zinc talon]

watch anything

[zinc talon]

idk bro, i watched ts in 9th

dawg

[patent gorge]

i m talking about India rn bro!

[zinc talon]

just search

[patent gorge]

okay

bruh ,i didnt find any one derving chain rule from scratch

thye all said just write them in notebook as notes or just learn them

by seeing subtitles

in english

[zinc talon]

BRO WHAT IS EVEN IN THE CHAIN RULE

its derivation is trivial

you just write dz/dy times dy/dx

dy cancels

[patent gorge]

oh sorry i mean msolty also for power rule

[zinc talon]

you get dz/dx

[zinc talon]

just use limits

square terms get ignores

[patent gorge]

okay so in which grade u r currently now bro?

[zinc talon]

you get power rule

wao

[zinc talon]

11th

[patent gorge]

did u know what does multivariable calc means?

[zinc talon]

yeh, its used in phyics

[patent gorge]

in 11th?

[zinc talon]

yeh

[patent gorge]

wtf

[zinc talon]

conservative forces check

gravitational fields

waghera

[patent gorge]

partial dervatives?

[zinc talon]

yeh

[patent gorge]

where?

[zinc talon]

bro i knew ts in 9th

💀🙏

[patent gorge]

bro r u kidding with me?

[zinc talon]

no

[patent gorge]

these r early graduate level topics

[zinc talon]

these come in phy olymps

hence usefull

tho not used in math

in high school

[patent gorge]

to even "understand" and writing cleanly partial derivatives ,you need the knwoledge of lorentz transform,fourier analysis ,and some real and complex analysis knowledge!

[patent gorge]

here u got catched!

[zinc talon]

umm, ig when working with real functions they are quite easy to understand

just small change in x taking y to be constant

smth like that

[zinc talon]

this is in the International Physics Olymp syllabus

[patent gorge]

Did u did Physics olympiad?

Wow bro, in india ,you get so much these stuffs! where did u learn these even from 9th?

[zinc talon]

nah i wasted my previous years playing

i just knew shit, i never practiced it

now im locking in and practicing

and grinding olympiad

[patent gorge]

when did u strt this vro?

[zinc talon]

9th ig

[patent gorge]

R u regretting over it or dancing ?

but u said u r being locked in now

[zinc talon]

i am regretting over me not studying

and practising

i couldve easily made it to camp in 10th if i practiced

[patent gorge]

So ,clearly ,you r being loecked like a mf in class 11?

[zinc talon]

bro locked in is a metaphor

that now i will start studying

srsly

[patent gorge]

but bro GPT buddy said

No. Physics olympiads do not require partial derivatives.

Official rule

The syllabus of the International Physics Olympiad allows basic calculus (ordinary derivatives and integrals), but the formal mathematics of partial derivatives is not required.

The syllabus explicitly states that students should know:

derivatives of elementary functions

basic integrals

simple calculus applications

But it also says that the “concept of gradient vectors (partial derivative formalism is not needed)”.

is he dumb?

[patent gorge]

wow ,How much ya till now?

[zinc talon]

partial derivatives are often used in olymp handouts

like knzhou

and kalda

and are done during training

[patent gorge]

what the hell is this knzhou ,kalda and handouts?

[zinc talon]

olymp training material

[patent gorge]

but they r not in slyllabus

anyways ,wht u wannan become?(currently doing Masters in maths!)

[zinc talon]

bro idk

[zinc talon]

i have no clue, i like math, chem and phy

evryth

prolly smth science related

[patent gorge]

Everything?

wb coding?

[zinc talon]

yeh

i did that

a while ago

[patent gorge]

did u takecoding in 11th?

[zinc talon]

na

honestly i can easily relearn eveyrth what the school even has to teach me

it wasnt worth it

[patent gorge]

So ,did u ever think ,choosing coding or CS as a proffesional?

[zinc talon]

i mean its fun

but i dont like sitting in front of the computer

all day

[tepid wraith]

hi

[patent gorge]

hello

[patent gorge]

So did you evr think gonna choose that black road?

[tepid wraith]

what are you all discussing? may i also come in

[zinc talon]

idk, ill see

[zinc talon]

studies

[tepid wraith]

i see

[patent gorge]

WHy does circle is continuos

[patent gorge]

Ahh man ! okay

btw how r u studying and learning in 11th now? aiming for?

[tepid wraith]

circle is continuous? doesn't it have a specified area?

[patent gorge]

wtf

R u were blind these Math years?

anyways ,it does

like pi is continuous

as it is a irrational number!

[tepid wraith]

my friend, what does continuous means in your book?

[patent gorge]

You can never "catch " circle under anything ,like nay other shapes

[patent gorge]

something happening smoothly

wihtout breaks

like butter

for example

AND circe is contnuous

You can search about it

ask anyone

[tepid wraith]

i see, so in your words "circle is happening smoothly"? right?

[patent gorge]

and evn aks an LLM

[patent gorge]

as it is not a fucntion of x !

it is a closed curve

I may give u prove of it

but not rn!

mmmm

[tepid wraith]

ah, my friend, relax, did i ever say you are wrong?

but here me out first, my friend...

in your words "circle is happening smoothly", keyword here is happening, meaning it's still going on...

what is still going on? 😅

[patent gorge]

it is descrbing a relation ,not a prcoess friend

actually you can never broke a cicle at all

if its not a ring

so its contnuous

common snese

[tepid wraith]

but the relation already existed, isn't it?

[patent gorge]

if u cant belive on it, you can look up to calc textbooks or geomtry textbooks too!

[patent gorge]

what relation ,R U talking abt?

[tepid wraith]

ah again my friend, you seem to think i'm not believing you

[patent gorge]

Actually vro ,first dont call me a firend ,its irritating

and another , AS whatver we do ,if we even use some basics of trig ,and even use tangent idea

we can get that circle is continous

[tepid wraith]

ok, how shall i address you?

[patent gorge]

as in whichever point you move in a parameter o a circle ,it never gives "nothing " or broken slope like in 1/x

[patent gorge]

you r being very polite than normal

anyways call me ONE

[tepid wraith]

isn't politeness the very integral part of having a thoughtful discussion? the one

[patent gorge]

yeah

you r right

[tepid wraith]

anyways

back to the discussion

again i'm repeating just what you stated before

circle is continuous because it's happening smoothly

and you gave the explanation behind your reasoning

[patent gorge]

Here smoothly means with no breaks and no "nothing" in the line

[tepid wraith]

ok ok, so...

what is this "vehicle" that has no breaks? do you get me?

[patent gorge]

unlike any other polygons ,circle species r very good

oh

[tepid wraith]

what is the thing you are saying that goes on in the circle?

[patent gorge]

vehicle means a full set of a multivarible function ,which includes many functions such as petrol,engines,motor,tire,breakers etc, and those all functions behaves diffrenty but are combine into one euquation

[tepid wraith]

i see

[patent gorge]

if u mean by tires ,then its another breed

[tepid wraith]

but here is another question. can an equation break? if yes what is it?

[patent gorge]

yes like 1/x , and here "break" means in graph and logic ,like when this equation 1/x , reaches 0 , then it gets a broke slope , as you cannot divide by 0

this is the most basic reason i can gave it to u

[tepid wraith]

okay, so in other words an equation for example y = x^2 is not breaking to you, right?

[patent gorge]

also like , can u solve x^2 + 1 /x^2 - 1 ?

Actually it also have a hole!

[patent gorge]

yes!

its a simple parabola

[tepid wraith]

so is y = x^2, also a continuous in your view?

[patent gorge]

you can check on desmos if u like

[tepid wraith]

One, again i'm saying to you, i'm not saying i don't believing you

[patent gorge]

yes only if its not x^2 / Z , where Z can touch 0

so if u ask x^3

yes

it does also a contuous

[tepid wraith]

okay then how about y^2 = x^2, is it continuous or not?

[patent gorge]

if u r not dividing it by some equation ,which "might" touches 0

[patent gorge]

its simply y = x , so its just simply a linear line

so yes ,it is also a con=tniuous

[tepid wraith]

now pause and think critically here

i'm not saying you are wrong again

i want you to think about it

[patent gorge]

look at desom , it makes 2 striaght linear lines ,looking like x

they r continous and linear

[tepid wraith]

i don't care what desmos is showing right now, i want to know what you think here

so what do you think?

[patent gorge]

lets try this anyway!yeah!

y^2 = x^2 only possible, if and only if y = x,if its not ,it gives contradicts and never talk to the graph, btu when it is THEN it is continuous,;lets sperate the ideas frist

we say f(x) = y^2 and g(x) = x^2 , when we plot this into the graph we get two parabolas, and actually when solving this in geomtry ,we get two squared shapes , and when we r stating that f(x) = g(x) , then it means those two square shapes r identical and twins and whereas those parabolas r symmetrical to each other and or congrunent to each other !, but the question again comes , that WHY does they r even symmetrical, in general we say anythign symmetrical because it "looks" identical and twin-like,

also if f(x) = g(x) , then f(x) -g(x) = 0 , but what if in x^2 - y^2 = 0 , we take a limit as ; lim (x-> 0) x^2 - y^2 = 0 , then it beocmes -y^2 = 0 , then also y ^2 = 0 , and if y^- 0 , then by x^2 = y^2 , we get both y^2 = 0 and x^2 = 0 , it means it doesnt show any lines , but WHY does it shows that!?

[tepid wraith]

Excellent demonstration but that wasn't the point of query

[patent gorge]

also yes ,"difference of squares" from high school comee in my mind rn!

[patent gorge]

r u challanging me to make new MAthematics?

[tepid wraith]

😕 ooff no not at all

Anyways

[patent gorge]

anyways , if x^2 - y^2 = 0 , then x^2 - y^2 = (x+y)(x-y) , then (x+y)(x-y) = 0, then x = - y by x_ y = 0 , and x = y by x-y = 0 , it means x is equal to both y and y , anyways its common snes e if we r squaring!

[tepid wraith]

What about -y^2 = x^2?

Is it continuous?

In your view

[patent gorge]

is it -(y^2) = x^2 , or (-y^2) = x^2?

because both have differnt meanings

[tepid wraith]

The first one

[patent gorge]

smart breed

[tepid wraith]

Pardon?😅

So?

Is it continuous or not? 😅

[patent gorge]

it gives yi = x

which is a complex number

[tepid wraith]

Yeah...and?

[patent gorge]

it cant eb plotted ina graph

its a uncontinous

[tepid wraith]

Ok fair enough

[patent gorge]

it is not mesaurable by any real system we have

becase squaring any number cannot give a negative number at all

[tepid wraith]

Now how about 1 - (y^2) = x^2???

[patent gorge]

,as there graph looks differnt on f(x) = -(y^2) and on g(x) = x^2 , and then saying f(x) = g(x) ,makes it yellling

[patent gorge]

its actually following a right angle triangle

following pythagoras

as 1^2 - y^2 = x^2 is same as P^2 = H^2 - b^2

[tepid wraith]

Are you sure? Just asking

[patent gorge]

yeah ,i may be wrong ,if yes ,it would be glas to learn from my mistakes ,as all made mistakes

but i can bet ,i m correct

becuase its obvious

[tepid wraith]

So is it continuous?

[patent gorge]

Waittttt

it also follows

x^2 - y^2 = r^2

its a circle formula

wtf i can foregt tht

but also wait pythagoras also applies on triangles

and whereas trignles r used in unit circle

so in a graph it forms a circle

with radius being Changeable

[tepid wraith]

I don't know 😀 so is 1 - (y^2) = x^2 continuous?

[patent gorge]

but if 1 -y^2 <0 , then x is the complex number

[patent gorge]

ofcourse as it isa circle radius , but actually if u look at the equation itself , and not on the formula or any graph shape

then let me think

[tepid wraith]

Think think, think very carefully, and also follow the questions I asked you before and the answers you gave earlier too

[patent gorge]

anyways i m writing the process , but why r u aksing me these?

[tepid wraith]

All will be cleared later, good one

So?

Also

No need to explain to me anything much, I know you know how to reach the answer

[eager copper]

Oh cool

[silver basalt]

yall got words from other languages that english doesnt have a direct translation for?
bc if so please i need a bunch

[ionic star]

случиться means to happen when the reason is unclear or doesn't matter, sorta like "come to pass"

although there are so many synonyms, maybe i'm missing one

occur?

[silver basalt]

occur means happen

[ionic star]

come to pass is closest i guess

god made it happen

[silver basalt]

some tree exploded with no warning
very случиться

i quite like this but i cant use it

[ionic star]

же is kind of like German doch, it means the sentence is important
In English it would be like emphasizing the copula
Он же психбольной
He is nuts

"for god's sake"

[patent gorge]

Here is the proofs (tryinh) that 1- y^2 = x^2 is continuous or not ,

[ionic star]

давно means far in the past, it's funny that English doesn't have this

[tepid wraith]

Hello

[patent gorge]

Here is the proofs (trying) that **1- y^2 = x^2 **is continuous or not ,

we start with x^2 = 1- y^2 , then finally x^2 + y^2 = 1 ,if we take H = 1 , B = y , P = x , then as we know h^2 = P^2 + B^2 , then x^2 + y^2 = 1^2 , if construct into triangle, with hypoteneuse 1 ;base x; and perpendicular side as y ,if we flip the triangle and think ........

.
. . y
1 . .
. .
..............
x

and first find the unknown circle's circumference around the triangle by thale's theorem as ,if Hypoteneuse is the diameter of that circle ;then r = C/2 , and here ; C was 1 ,then , r = 1/2 ,which is 0.5 = r; Which means the initial point at exactly where that bottom of that hypotenuse is then increasingly it exactly 0.5 up in the y axis with respect to x axis , we got our radius of a circle!, Which also says ,its area is pi , and if r = 0.5 = (x^2 + y^2) /2 , then 2pi((x^2 + y^2) /(2)) = a ,then which gives pix^2 + piy^2 = a , then x = sqrt(( a - piy^2)/pi) ;putting this x value into x^2 = 1-y^2 , we get , (sqrt(( a - piy^2)/pi))^2 = 1-y^2 ,which is (a - piy^2 )/pi = 1-y^2, which yields a- pi^2 = pi - 2piy^2 ,which gives exactly again a = pi , which explains itself as it is again ; a = pi only; We get nothing from this;

[rich moat]

[tepid wraith]

You can use latex bot here, you know

[silver basalt]

i know the german doch
i compare it to "shit"
depending on context and emphasis it can mean "very" or "not at all"
this is doch good

[silver basalt]

hmm true that is strange

we also didnt have overmorrow for quite some time but it got repopularized

[ionic star]

German just says "long" without "ago"

that's cute

[silver basalt]

oh weird

[patent gorge]

if x^ = 1-y^2
then y = sqrt(1-x^2) ;but we would stop using algebra and start using geometry now! let's imagine a square of x^2 and y^2 and 1^2 , and now we r saying A x^2 = A 1 ^2 - A y^2 ,(NOTE - here A means a single word describing "a" square or "a square"!)

if we combine the sqaure of y^2 and 1 ^2 into one then!

...............................
. .................... .
. . . .
. . 1^2 . . y^2 (whole square shape is y^2 as an area first!)
. ................... .
. x^2 .
.................................

so it means by x^2 = 1-x^2 , gives us

x^2 only(shape,){I cant draw here because it would take a lot of time then!}; anyways try it numerically then;

[tepid wraith]

Very good demonstration

Were you making this all these time ? 😅

....

Is that a yes?💀

[patent gorge]

if we do that in numerically then; x= 5, y = 6; x^2 - y^2 = 1; then 25 - 36 = 1 , hence 11 is **NOT equal **to 1 which is not being true; if we solve this once again as x = 2 , y = 1 ; 2^2 - 1 = 1 ,then 3 is **NOT equal **to 1

lets say if we try quadratic equation ; x^2 - y^2 - 1 = 0 ,then for x ; x = (y +- sqrt(y^4 + 4))/2 ; and for y as , y = -x^2 +- sqrt(x^4 + 4))/-2 ; then y = (x^2 -+- sqrt(x^4 + 4))/2 ,if we solve it further on x ; 2x -y^2 = +-sqrt(y^4 + 4) ; and then if we did the same for y ; x^2 -2y = +- sqrt(x^4 + 4); it means 2x-y^2 = x^2 - 2y ; which yields ; x^2+y^2 -2y -2x = 0; but also , x ^2 -y^2 -1 = 0 ; then x^2 +y^2 -2y-2x = x^2 + y^2 -1............. then; 2y^2 - 2y -2x + 1 =0 ; which gives y^2 - y - x = -0.5 ; (yeah i skipped some algebraic steps, but as am assuming the reader to know atleast high level math only!) ;then x+ y - y^2 = 0.5;

Hence we get another expression as ;
x+y -y^2 -0.5 = 0 ; then -y^2 + x + y -0.5 = 0 ; then by doing and applying tottaly quadratic equation in it we get y = (x+y -+- sqrt(x^2 +y^2+2xy -2))2 (I assume b = x+y) although if we plug this y value into x^2 - y^2 = 1 then;

we get;

x^2 - ((x+y - sqrt(s^2 + y^2 + 2xy -2))/2)^2 = 1 OR x^2 - ((x+y + sqrt(s^2 + y^2 + 2xy -2))/2)^2 = 1

then;

x^2 - ((x+y - sqrt(s^2 + y^2 + 2xy -2))/2)^2 = x^2 - ((x+y + sqrt(s^2 + y^2 + 2xy -2))/2)^2 = 1 ;

if we solve for both sides then taking S = x^2 + y^2 + 2xy - 2 ,thn we finally got

As we would compare LHS and RHS factored values then ; x^2 - xy + ( -x^2 - y^2 + 1 + sqrt(S)(x-y))/2 = x^2 - xy + ( -x^2 - y^2 + 1 - sqrt(S)(x-y))/2 which is finally sqrt(S) (x-y) = -sqrt(S) (x-y),them simplyfying gives us; 2sqrt(S) = 0 , then it means sqrt(S) = 0 , then it means ost probebly x^2 + y^2 + 2xy - 2 = 0 , then it means either x OR y have to be 0 here , I can;t solve this more here ;because if x and y are either 0 then IDK;;;;;''''

[tepid wraith]

Sigh

If I knew you would do this I would have never discussed this, you didn't have to waste your worthwhile time just to prove to me it's continuous

But anyways I appreciate your efforts

[patent gorge]

no bro, i just spend only 1hours and 15 mins on this topic only! and this alos encourages my mathematicla skills to be fresh down

btw there is more

like 2 pages more only

Can i write them?

[tepid wraith]

Latex bro

There's a latex bot here to make your proof very good

[patent gorge]

ahh,i m new to latex , i just know VERY basic latex ......

[tepid wraith]

Okay I see

[tepid wraith]

Well if you want, sure, I'm reading it

[patent gorge]

i m trying to learn it on overleaf and on other platforms 'maybe sooner i would be a GOD in latex

[tepid wraith]

But I think you are really very clumsy when it comes to thinking

Can you stop writing for a moment? And listen to what I have to say? Maybe it will help you

[patent gorge]

ok

i m stop

yeah ,i may look clumsy for a bit

But im obesses over WHYs

espescially ones which is beyond my scope and lvl

recreating maths is what ia lways try to do'

[tepid wraith]

This whole paragraph is useless,
x^2 + y^2 = 1, it is the equation of the unit circle bro, unit circle means radius = 1, which means area would be pi, that's it

[patent gorge]

but humans takes all places on exact evrrything ,its almost impossible9i m saying its possible,yes its possible!) to make a new mathematics !litreally!

[patent gorge]

ik

but i dont belive it!

Why would it be even

who says it to be like tht

[tepid wraith]

No one because it's already a common knowledge in maths

[patent gorge]

ik its just VERY basic idea

[patent gorge]

ik,

[tepid wraith]

Then why did you have to write a whole paragraph just to say, that area of a circle made by unit circle equation is pi?

Also, how the area of the circle plays a role in determining whether it's continuous or not?

[patent gorge]

because ,maybe noone reads my parahgraphs ,i was actually trying to remake it or even challanging the equation's ideas itslef by many observers by Maths itself ,as i uses different tools as Algebra,logic,Numerically,graphicallly,Calculus(via limits) , formula,Definiion(recreating it) ,etc!

[patent gorge]

becuae of pi

pi is irrational

[tepid wraith]

You are not making any new math here, my friend, you are stretching it in a roundabout fashion

[patent gorge]

oo

ok

btw wht u wanna tell me at the end

[tepid wraith]

What I want to tell is that, you can just simply intuitively prove that circle is continuous without using any sort of higher math

Imagine you are holding a pencil

And you are drawing a graph of anything on the graph paper such as

y = x^2 + 1

Can you draw the graph without lifting your pencil?

If yes then it's continuous (over the range of x available in the graph paper)

If no, then it's not continuous

[patent gorge]

o

shit!!!!

cOMMON SENSE

[tepid wraith]

if you draw y=1/x graph, you have to lift your pencil at x=0

[patent gorge]

oh sorry,for me wasting ur time

btw it was fun tho

[tepid wraith]

No no

My time isn't wasted

[patent gorge]

i will use logic and COmmon sense another time!

[patent gorge]

o

[tepid wraith]

Similarly for any circle, you can draw it on the graph paper without lifting up your pencil

Lifting up your pencil = the break you were talking about at the beginning

[tepid wraith]

Anyways you may continue your proof

I know you were giving your best effort here

You were serious

So I won't mind reading the rest of your proof

[patent gorge]

leaveit bro

relax

sleep

calm

chill

and at the end ,do maths

and be healty and fit(strong,muscular!)

gn

......

btw still i will write it

[tepid wraith]

Nah man, write it down

Finish what you started

[patent gorge]

MoTiVaTiOn🔥

okay?

ok

[tepid wraith]

Do it, but no need to rush

[patent gorge]

Thanks; Sir

Now again; if x^2 + y^2 = 1 ,then hypo is 1, base is x , p is y ; but using the formula x^2 + y^2 = r^2 , but our r was 0.5 ,then this hsould nnot be also true , which then this proves tht it is not contuous ,as all the polynomilas are known to be Continuous,expect dividing an expression by soemthing else which "can" be 0; Now if we do x^2 + y^2 = 1 , by graphically then x^2 graph i a parabola whereas y^2 graph is also a parabola,it means x and y should be less than 1 ; As x increases ,y decreases; and vice versa,and they should never be equal ,if we change the hypoteneuse of this right angled triagle then the circle forming on the graph could also then gonna change!

[tepid wraith]

....

Now that I'm reading it....

You did a lot of mistakes!

[patent gorge]

if we try to do it with calculus then; x^2 + y^2 = 1, then lim(x->0) x^2 + y^2 = 1 then y^2 = 1 then it is only possible if y = 1 ,which also restrict itself , and if lim(y->0) x^2 +y^2 = 1 ,rhwn alos then it is also being restricted , and now make them equals to 1 either x and y have to be 1 or 0 ,
Now if we try to do it with as formulas then as we already know tht in x^2 + y^2 = 1 , but stillwe would end up getting the same!

[patent gorge]

wth

spelling mistakes?

[tepid wraith]

This paragraph has mistakes

[tepid wraith]

No, math mistake

[patent gorge]

lemme see

[tepid wraith]

Bro

[patent gorge]

oh yeah i assume x^2 - y^2 = 1 ,instead of x^2 + y^2 = 1

[tepid wraith]

x^2 + y^2 - 1 = 0 is not a quadratic equation

And you used the quadratic formula on a non-quadratic equation

[patent gorge]

yes ,i did tht on purpose to see how does diiferent signs on expressions whole meanings!

[patent gorge]

wht?

x^2 + y^2 = 1 ,is non quadratic?

i assume y^2 AS A PARTICULAR number

[tepid wraith]

x^2 - y^2 - 1 = 0 is not a quadratic equation so you can't use the quadratic formula

[tepid wraith]

No you didn't

[patent gorge]

sh*t!

yeah yeah i got it ,it was ax^2 + ax+ C = 0 thm

[tepid wraith]

If you considered it then x^2 - (y^2 +1) = 0 will become in this form x^2 - c = 0(I let c = y^2+1)

[patent gorge]

oh i fogot it

[tepid wraith]

x^2 = c, then x = +-sqrt(c)

Now substitute the value of c

x = +- sqrt(y^2 + 1)

That's the solution

[patent gorge]

ik

[tepid wraith]

You did everything wrong in that paragraph

[patent gorge]

but if we try to substitute it in x^2 +y^2= 1,it would be mosnter

[patent gorge]

GOt it

[tepid wraith]

You cannot bro that's not how it works

You cannot apply quadratic formula in an equation of two independent variables

[patent gorge]

wht? acutally doesnt we can susbtitute x = +- sqrt(y^2 + 1) into x^2 + y^2 = 1?

[tepid wraith]

No

....

[patent gorge]

why?

[tepid wraith]

My god

[tepid wraith]

Because that's an entirely separate equation and you deduced x from x^2 - y^2 - 1 = 0, not x^2 + y^2 = 1

[patent gorge]

oh so thts

Oh i understand

i thought it was from x^2 +y^2 = 1

[tepid wraith]

...

[patent gorge]

miunderstandment

Nico brother

Nice to meet you

[tepid wraith]

I would say this is blatantly wrong

[patent gorge]

good luck big boy.?

[patent gorge]

so whts that?Misunderstood-ness?

[tepid wraith]

Thank you for the best wishes

[tepid wraith]

You didn't misunderstand, you did it all wrong knowingly

[patent gorge]

yeah

i will imporve

but bro in which things u might think ,i should be get good at?actually?

Dont be LLM for this

[tepid wraith]

Honestly... You are good at nothing 😅 (I'm talking about math only) you have a lot to improve

[patent gorge]

like!?

[tepid wraith]

Everything, I think you need to start with basic school level algebra

[patent gorge]

its not possible

i m not tht much kid

anyway ,i appericate your guidiance

[tepid wraith]

I don't know, the more I read your paragraphs, more I see your faults

Like you just know those concepts but cannot apply it correctly

[patent gorge]

i understand it now

where my fualts r

[tepid wraith]

You have to conquer the basics

You cannot use any formula on anywhere

Every formula in math has certain conditions

Where you can apply, how to apply and if it seems like you can't apply it then how to make the problem in a form where you can apply it

[patent gorge]

i will 100% impove in just 1 year , and will try to reach undergraduate lvl or beyond sooner!

[patent gorge]

oo

[tepid wraith]

x^2 + y^2 = r^2, so r is the radius man, and radius is equal to 1 in unit circle, how did you even got 0.5?

Your proof is false at it's core

Sorry if I'm being very direct

[spare pivot]

Silence the answer is 0.67

[patent gorge]

so ,

1.) i should need to learn how to make proofs
2.) i should make my basic maths strong
3.) i should learn latex for serious commmunicatons

[tepid wraith]

You just wanted to say those two digits, well done 👍

[spare pivot]

Omg so smart and observant

[patent gorge]

and 4.) last but not least(popular line) i should give up my ego on maths'

[tepid wraith]

Latex is for writing proofs

Not communication

[patent gorge]

hell shit'

[tepid wraith]

How old are you? If you don't want to share that then can you atleast share whether you are in highschool or uni/college?

[spare pivot]

Kindergarten

[tepid wraith]

Ngl, it's possible

[patent gorge]

gae doesnt matter nor school

curiosity matters more than tht

I m learning far beyond wht my shcool would ever teach

[tepid wraith]

Okay, I got it, it's kindergarten 😆

[patent gorge]

and the basics u were talking abt ,were my commonly rushed mistakes

Notmy daily routine mistakes

[tepid wraith]

Just joking

[patent gorge]

i am improving'

even u K.D

yes you,you should be a begginer and "kid" in maths well before

Everyone was like this

even eisntein,terence tao too

EVRONE

it doesnt mattters with age at all!

[tepid wraith]

I doubt about those two

[patent gorge]

ok , but ummm(oh gossh everyone has brains!)

[tepid wraith]

Excluding the exceptions, yes it does matter

[spare pivot]

@patent gorge lowk right

[tepid wraith]

Not everyone is Einstein or Terrence tao

[patent gorge]

bUT ONE CAN BECOME LIKE THEM

but KD r u an undergraduate?

[spare pivot]

No

[tepid wraith]

I don't know

[tepid wraith]

I have already graduated

[patent gorge]

THEY CAN!

idk but my cant mind accept tht they cant

[spare pivot]

Are you obsessed with maths

[patent gorge]

did u know wht u typed?

[spare pivot]

I'm asking

[patent gorge]

damn,its maths disguised as texts!

now u know

[tepid wraith]

Obsession is okay, but he is making mistakes

Atleast correct them

[spare pivot]

Obsesion is literally the best thing to have if you want to improve

[tepid wraith]

Not really

[patent gorge]

ik

[spare pivot]

Yes really

[patent gorge]

it was"rushed"

[tepid wraith]

Nope, at least that's not for me in my case

I'm not obsessed with maths yet I improved

Still improving but again not obsessive

[spare pivot]

If you were obsessed you would know more than you know by now

[patent gorge]

but guys,everything aside , At the end ,no one knows everything

[tepid wraith]

1hr 15 mins, yes it was rushed

[patent gorge]

even 3blue1brown doesnt

[tepid wraith]

Maybe, but I'm fine with what I have learnt

[spare pivot]

Is maths really that serious

I joined for the tag

[patent gorge]

yea'

[spare pivot]

And emojis

[tepid wraith]

But 3blue1brown doesn't make silly mistakes and incorrect use of math 😅

[old oak]

Mathematics is a very serious discipline, the people who do mathematics are often not serious.

[patent gorge]

who knows

[old oak]

There's a lot of people in this server with great sense of humour and fun

[spare pivot]

https://tenor.com/view/who-is-he-who-is-that-peppa-pig-gif-13606975557282567491

[patent gorge]

he only sees his correct things ,never his mistakes

[spare pivot]

Bruh

[tepid wraith]

Unless it's your major, I don't think so, you just learn what's necessary for you

[old oak]

There's also a lot of babbling inadequates and unpleasant assholes

[tepid wraith]

Everyone knows that

[old oak]

In conclusion, the mathcord is a land of contrasts

[tepid wraith]

Because there are no mistakes in him lol, he can be inaccurate but not incorrect/wrong

Anyways

@patent gorge how old are you anyways? This is not related to this, I'm genuinely asking

[spare pivot]

Why do you want to know tho

[tepid wraith]

Just asking

Everyone here asks me and other people this question

[rocky shuttle]

It's just part of the discord age verification system

[tepid wraith]

I thought he thinks I would judge him, so just to clarify I will not

[patent gorge]

15...(turning 16 in April this year!)

[tepid wraith]

I see

[patent gorge]

Btw you will know about me in the future ,but not as my discord name as it is rn,but tottaly differently name from somewhere else!

I m not fantasizing at all

its reality

and you?

[tepid wraith]

Okay

[tepid wraith]

Me what?

[patent gorge]

age ?your age?

[tepid wraith]

22

[patent gorge]

Wohoo

wht r ur aiming for?

[spare pivot]

Should I learn maths 😳

[patent gorge]

i can also lie my age btw

But i dint.

[tepid wraith]

Nothing as such, i'm just moving in a dark

[patent gorge]

means?

Batman?

[spare pivot]

Super mysterious

[tepid wraith]

It means I'm not sure about my future

[old oak]

I don't think so

[spare pivot]

Why 😡😡😡

It looks easy

[old oak]

The images you're posting suggest you might not have the creativity required

[patent gorge]

Oh buddy,r u indian?

[tepid wraith]

No

[spare pivot]

I have enough creativity to express myself

[patent gorge]

Oh sorry,anyways!

Good luck for your future buddy!

nice

gn

[tepid wraith]

Good night

[spare pivot]

gn

[patent gorge]

its 3:09 AM here

[spare pivot]

11:39 pm for me

[patent gorge]

https://tenor.com/view/employee-appreciation-day-employee-appreciation-staff-appreciation-employee-recognition-team-work-makes-the-dream-work-gif-11919604255277794622

[spare pivot]

Heh now you quiet heh ik ik I got you

[tepid wraith]

You will know that after you learn maths

[patent gorge]

r u talking to urself?

[spare pivot]

I'm schizophrenic

Weren't you going to sleep

[patent gorge]

u r interesting perosn

And Intersecting too

wht happens?

[spare pivot]

Maths looks pretty easy if I understand it 😳

[tepid wraith]

As you wish

[spare pivot]

What type of math is the hardest for you

[tepid wraith]

Every math is hardest once you dive deep into any topic

[spare pivot]

This did not answer my question

[tepid wraith]

It does

[patent gorge]

try to learn generating functions

[spare pivot]

Go to sleep bro

[spare pivot]

Is there any that you don't understand yet or is hard for you

[tepid wraith]

All I can say here is, I know many math but I don't know every and all math, that's it

[patent gorge]

no

[spare pivot]

Stop with the philosophy Bs I'm genuinely asking if there's something you are trying to learn or you don't understand yet

[old oak]

No one does

[tepid wraith]

sigh I don't understand math yet, is that an okay answer for you?

[tepid wraith]

Yes

[spare pivot]

The avoiding 😭

[foggy sinew]

Hello, I am a neurodivergent (AuDHD) who is inexperience with social platform and therefore it would act differently than most people (in other words please be mindful of that), and I use speech to text a lot because spelling is not my strong suit, anyway I joined this server through a user tag because I like math, it's a lot more logically consistent than English (which appeals to my brain of wiring) I'm hoping to have a little bit fun in this community every now and then.

[foggy meadow]

It's so over and it's so back cycle is cycling.

[steady pagoda]

what kind of math do you like

[foggy sinew]

no one ever asked me that particular question before, I guess anything that's before precalculus stuff.

[delicate sundial]

oo cool, like algebra type stuff?

[foggy sinew]

my associative thinking can't recall the connection with the term algebra, all I know is I connect to it better if you explain the concept and what each purpose specific function how to fill that formula, English I struggle a little bit more then math.

[delicate sundial]

Oh I see,

[foggy sinew]

sorry if I'm using some fancy psychological term I am been slowly mapping my mind with the help of an AI chat, and I learned to have a hyper/high associative thinking which explain why I am able to recall such niche or random piece of information on the related topic.

[sour sky]

hellos

wow discussion is big so i'll ask here

is set theory math

but howww

i feel stupid asking it but isnt math js numbers & also looking for numbers cuz of algebra

or wait

geometry too

hhh :<

[steady pagoda]

https://en.wikipedia.org/wiki/Euclid's_Elements

[delicate sundial]

i mean set theory deals with more the concepts of math, i mean, just take a look at like abstract algebra or something

especially in hgiher math you see less and less numbers and more and more elegance, proofs, and such

[sour sky]

oh

ic

[keen nimbus]

Math getting harder everytime

[true tapir]

and you're getting stronger

[digital furnace]

Omg it's him

[tardy sigil]

Hello.

I'm new here

[keen nimbus]

Leveling up with this one

[gray glade]

i do think getting in touch with numbers and applications from time to time is important in your math journey

physics classes

[visual rivet]

YO is pre calc by prof leonard good if im starting from scratch ??

[round abyss]

see if it works for you

[bitter pier]

https://youtu.be/_vX09m9lixYthis is damn!about topology

[gritty heath]

Please try to refrain from posting links in multiple channels

[rich moat]

sometimes I wonder if my university offers undergrad research positions

that would help with my grad applications

especially since I failed a few times

[placid basin]

I got into grad school guys!!!

[acoustic field]

congrats!

[gritty heath]

Nice

[steady lodge]

Dub

[placid basin]

Thanks!!!

I’m lowkey scared

[mental vector]

I was watching reels and some guy did (23x17) like this

20x20-3²

How?

[acoustic field]

difference of squares

[gray glade]

23 * 17 = (20 + 3)(20 - 3) = 20² - 3²

[unborn sandal]

Congrats!

[eternal prawn]

math dummy here, why ln uses euler number instead of a more useful and precise base like 2?

[junior veldt]

It’s cause it links directly to calculus

2 is to discrete change as e is to continuous change

[latent edge]

because in many cases e is more useful than 2

[zealous bronze]

because e is the groupoid cardinality of the finite sets

[latent edge]

I hate that I know this joke

My prof once said it

[magic python]

e? e is very useful, I'd know.

[idle steppe]

Because e naturally shows up in differential equations like y'=ky

Not the only reason for sure, just one reason

[calm fulcrum]

$\frac{\dd}{\dd x}\ln x=\frac1x$ is one reason why (if $\ln$ used another base like $2$, this wouldn't hold)

[fathom swallow]

nadat12

[loud seal]

🔥🔥

[true zinc]

is it true?

[odd pulsar]

$\lim_{n\to\infty} n^{1/n}$ = 1

[fathom swallow]

GravitilessUniverse

[odd pulsar]

why?

it shouldnt be hard to prove tho right

[calm fulcrum]

ye

[fathom swallow]

nadat12

[odd pulsar]

oh yeah

ofc

some asymptotic comparison ofc

its intuitive but you always have to rewrite it in a way that theres a formula you know

which is ln(n) = o(n)

its kinda annoying though that you cant just use intuition

[calm fulcrum]

lhopital :DDD

[calm fulcrum]

it's not very hard to prove tho

[odd pulsar]

do you have an idea about that famous formula for e = lim 1 + 1/n to the n

why is it that we cant just apply the limit to 1/n which is zero

and then say its 1 to the n

[spice grotto]

i'd say it's cuz generally lim (f(n)^g(n))=(lim f(n))^(lim g(n)) is true when both limits exist and are finite

[calm fulcrum]

because that's not how limits work

you can prove rigorously that the limit must be in between 2 and 3

[odd pulsar]

i see

thanks

[calm fulcrum]

and lim f(n) is positive

you can prove this rigorously by applying limit chain rule on e^(g(n) ln f(n))

[spice grotto]

right yeah

[odd pulsar]

ur definitely taking a real analysis course aren't you

[calm fulcrum]

no i've never taken real analysis

lmao

[odd pulsar]

daym

but like

rigorous is synonym of analysis in math

[brazen parcel]

Sup

[true tapir]

!bnuuys

[digital furnace]

!bnuuys

[sour sky]

ooo bunni

!bnuuys

yeyyy :3c

[polar adder]

!dinosaur

[digital furnace]

!bnuuys

[wild lantern]

Move to #bots rather than spamming this kind of thing here pls

[fresh comet]

[calm fulcrum]

hi gher

[tropic helm]

https://www.youtube.com/watch?v=sI_o8GxoR8w

[grim flax]

I might be addicted to dihydrogen monoxide….

[calm fulcrum]

shoot, i'm kinda addicted to dioxide...

[timid bronze]

I just realized daylight savings time starts tomorrow

Yay I fucking hate standard time so this is good news for me

[grim flax]

Doomed

[chilly totem]

5th april?

[timid bronze]

March 8th

[chilly totem]

In Australia i thought its april o

[timid bronze]

Ohh

[chilly totem]

https://tenor.com/view/kangaroo-australia-gif-5569301945329905539

[cobalt laurel]

@snow delta

[long marlin]

Hello discussion 2
I'm from discussion 1

[cobalt laurel]

hello discussion 1

[long marlin]

What y'all doscussing here and how many online

[frigid elk]

my math is weak

somebody help

pls

[round abyss]

if you have a specific question to ask, go to #❓how-to-get-help

[visual palm]

Skill issue

[odd pulsar]

bruh all my life im studying math and just today i've come to hear that ln(-1) = πi wth

mathematicians really love to get complex number in the party

[agile fiber]

if you've seen e^(i pi) = -1 that's just repackaging it

[odd pulsar]

exactly i have known that for like 3 years lmao

but its not like i understand that either

[night basin]

Finally a channel without occasional politics and philosophy

[rocky shuttle]

role...

[keen nimbus]

Bnuuy

[cedar creek]

Ts is gonna sound stupid but how do I study?

Srs

I need this info pls I'm begging ye lads 🙏🏻

Oh, thanks :D

[restive mirage]

Har ek gel milde vichaar ni
Tera yaar chale samjh te bahar ni
Chhora baaz bairi titra ki daar ni
Mere hatho dekh hone hai shiqaar ni

[stuck silo]

?

[frail gull]

Hello i need help for my mathematics prépa

Go to the mp ?

[restive mirage]

Not everyone who meets me can understand my thoughts.
Your friend (I) thinks beyond normal understanding.
This guy is like a hawk among enemies who are like small birds.
Watch, the hunt will happen by my hands.

[stuck silo]

Is taht a quote?

that*

[restive mirage]

Yah

That is lyrics

Of haryanvi rap song

[frail gull]

Help me please

In my forum

Mathematics

[stuck silo]

What other songs do you like?

[restive mirage]

Gangster type song

Leak bheed sava lakh ka glassi’aan me
32-Bore mila parso talashiyan me
Suit karda nahi weather re bahar aala
Hawa jail ki likhi aa meri rashiyaan me

Teri chadhdi jawani mera para gori
Karwa ke hatega koi kara gori
Chandigarh seize kare hariyane aale
Tedhi aankh te ton kar tu ishara gori

[stuck silo]

So hip hop and rap?

[restive mirage]

Yah

T20 match stared

New Zealand 153 runs in 54 balls

[cerulean crypt]

Wsp discussion 2

[noble tinsel]

nothing is up this channel is dead

[cerulean crypt]

I can see

[true zinc]

<@&268886789983436800> posting non english song lyrics

[fresh comet]

@frail gull @stuck silo welcome to the mathcord!!

[lethal sphinx]

hii

someone pls talk to me

[surreal sapphire]

hi

[lethal sphinx]

whats up with everyon

you guys are on the low or what

[shadow palm]

Hello nerds and turds

[tepid wraith]

what happened?

[lethal sphinx]

how are you

[lethal sphinx]

i dont know everybody are just quite

[tame egret]

This channel is just peaceful most of the time.

[tepid wraith]

everybody's grinding 🔥

[lethal sphinx]

when i first came here it was loud

[lethal sphinx]

lol

[visual palm]

hello discussion 2 nerds

[calm fulcrum]

ner;d

[lethal sphinx]

hello cheese

[cursive bramble]

Hi

[cedar creek]

hi!

[neat lintel]

https://www.reddit.com/r/math/comments/1rocna6/thoughts_on_the_future_of_mathematics/

another AI-fear based r/math post to ruin the day

I'm starting to think these are bots or just some kids thinking AI could replace any job

[unborn meteor]

hi

[lethal sphinx]

hii

[unborn meteor]

hiii

[lethal sphinx]

how are you

[hot forge]

Hi guys, should I take the SAT or the ACT?

[unborn meteor]

good

[shadow palm]

@brave flare is a mod.

[stuck silo]

Hey, I'm studying for the SAT rn. So SAT

[calm fulcrum]

sat is harder but shorter and more time

act is easier but longer and less time

depends on your testtaking style tbh

my parnets wanted to sign me up for act but i said no

[tepid wraith]

why not give both?

just asking

[rigid lion]

But I love talking

What am I without my identity to shitpost

[velvet dagger]

Just not the word "anything" fr

[stuck silo]

You can do other stuff to build upon your identity

[magic sleet]

Can you build upon identity?

[stuck silo]

You and Angelo are the same person?

[stuck silo]

Yes!

[magic sleet]

I mean that doesn't make much sense? Isn't your identity fixed? If you "build upon it" that is a different identity, a different person?

Unless you have multiple identity disorder or smthing

[rigid lion]

No

[magic sleet]

Hahaha, i have multiple left identities

(consider the function from RXR to R define by (a,b)->a)

[fresh berry]

take whatever you're more confident in both are tests for american colleges but generally I'd take SAT because of how easier it is (less problems, more time) than the ACT (Alot more problems and lesser time) while being more recognised across the world

[magic sleet]

Oh, can you?

[fresh berry]

it requires money to pay to take a test from SAT or ACT

maybe he doesnt wanna spend too much

[tepid wraith]

i see

[stuck silo]

What are invertible elements

[stuck silo]

Why?

[tepid wraith]

can you tell me how much does it cost?

if we take both exams

[fresh berry]

~200-300$

for both act and sat

[tepid wraith]

💀

[fresh berry]

im serious

[tepid wraith]

okay now i get it

[fresh berry]

like

idk why its alot

but it is what it is

[fresh berry]

yep

[cedar creek]

https://www.youtube.com/shorts/A5-pbbQ072U @loud seal smash?

[hollow cosmos]

Guys how is
a/1/b =ab

[magic python]

Exponent properties

The first can be rewritten as a(b^-1)^-1

Then the two -1's multiply to make 1

[unborn meteor]

,, \frac{a}{\frac{1}{b}} = \frac{ab}{\frac{1}{b} \cdot b} = \frac{ab}{\frac{b}{b}} = \frac{ab}{1} = ab

[magic python]

So it's ab

[fathom swallow]

speedydelete

[magic python]

That works too

[hollow cosmos]

So b will first go into numerator becoming a/b^-1 and then go again to numerator becoming ab

[hollow cosmos]

Wait what

[hollow cosmos]

umm i don’t understand

[magic python]

I can't explain it sadly

[ancient frost]

so u divide a thing by a fraction of a person

[magic python]

But that's literally a/(1/b)

[ancient frost]

then the whole person get b * whatever the fraction got

[hollow cosmos]

Ok

[hollow cosmos]

Let’s leave it nvm I’m not getting this my brain too slow

[lapis turtle]

think about dividing by 1/b, as multiplying by its reciprocal . the reciprocal of 1/b is just b/1 (i.e b)
so a multiplied by b is the same as a divided by 1/b
to give you a numerical example: 6 divided by 1/2 is the same thing as 6 multiplied by 2

multiplication and division are inverse operations, when you divide by a number you are simply multiplying by its reciprocal

[desert sigil]

hallo, can someone explain what the localization of a ring is in baby terms for my peanut brain

this is litteraly what Vakil said lmfao

[restive solstice]

Please what's 1 plus 1 im stumped

[lapis turtle]

As an example, say you have the ring of integers
This ring is not closed under division (if we have 5/2 it does not yield an integer)
What we do is we basically expand this system by picking some numbers and saying, hey these numbers are actually valid denominators
For example I want to allow division by powers of two so now my new ring can also include 1/2, 5/6 etc

[desert sigil]

Id suggest starting with adjoint functors

[restive solstice]

😭

[desert sigil]

or equivalently, just say cuz yonnema theorem said so

[lapis turtle]

yoneda?

thinks 💭

[desert sigil]

ya thats what i meant lol

I forgor spelling

[lapis turtle]

then you rembered....

[unborn trellis]

Invert everything in a multiplicatively closed subset

[desert sigil]

anyways i put myself in a fun situation, Im an engineering student first year of undergrad and decided to pick up math as a hobby, but then i decided to torture myself by picking up Vakil before learning basic ring theory :>, i know what a ring is but i dont know any of the basic theorems lmfao.

reason? idk its fun

[unborn trellis]

In terms of spaces, functions on open subsets around a prime ideal correspond to rational functions with denominators in the ideal

So for example, on the complement of a vanishing set of a polynomial, you have rational functions with 1/f

[desert sigil]

lawvere coded

[unborn trellis]

Oy vey

May I recommend reading maybe 2 chapters of atiyah-macdonald commutative algebra first

Perhaps ... 3 chapters

[desert sigil]

that could help

[unborn trellis]

Although I think vakil develops a lot of the algebra as you go

It's just slow

[desert sigil]

chapter 1 of vakil does throw you into the fog, but its pretty self contained

[desert sigil]

I think im confortable with being confused and rereading the book a few times. right now im focusing on defining algebraic objects by their universal properties on a first read

[unborn trellis]

That's a good route, although you should understand both a construction as well as it's universal property

Otherwise you don't even know that you have a representing object

Like if all you knew of tensors was the universal property that'd be tough

[desert sigil]

for some reason the abstractions make more sense to me lol. Ill defintely make sure i dont limit my exposure that much

[desert sigil]

tensors are a bit more intuitive IMO, if you get the idea of a product and its unique factorization no

but ya AG seems to be a mutli-year journey you just gotta start somewhere.

[unborn trellis]

Yeah definitely

I found when I took it that the geometry was actually the easy part and my algebra was lacking, so I thought it was very helpful checking the stacks project frequently

(I am not an expert take this with a grain of salt)

[desert sigil]

ya im self learning it rn and its prob gonna involve alot of making proof drafts and revising them over time and reading alot on this subject

while im not an undergrad math major, im planning to do grad school later in life with say a good GRE subject test score and transcripts on Real analysis and algebra.

fortunately the math community is a meritocracy that aknowledges skill from any backgroup for the most part

Hell yeah

What book are you studying

Nice, I just started a week ago honestly

Any tips?

Got ya, I myself have not done Comm algebra and learning it from the book

We should add one another to discuss our progress on the book or for any references

[light thorn]

only a few hours left to study for my Calc 2 exam tomorrow while I'm still stuck doing homework for it, while I'm already neglecting all of my other classes
I really don't know what to do anymore, I can't keep up with anything
Haven't had any time to study before, I am gonna fail

[calm fulcrum]

dang

what do you need to study, anyway

[light thorn]

Work, volumes, center of mass, parametrics, arc length, polar curves, sequences, some other stuff

[proven rose]

is anyone in university studying engineering, If u are what are u studying?

[desert sigil]

Electrical!

[proven rose]

where are u stidying at right now?

[desert sigil]

Community college🥀

Im not exactly the most important student 😭

[proven rose]

in what country?

[desert sigil]

US

[neat lintel]

Me too don’t worry

Also in the U.S.

California wbu

[timid bronze]

Chemical but I have not taken my major courses yet

I start taking my major ones next semester

Thermo 😟😟

[neat lintel]

Thermodynamics?

That’s a tough one

Good luck

[timid bronze]

I only hear horror stories about it 😭

Have you taken it?

What do you think