serious-discussion

[fervent pebble]

bad wew

[sleek wing]

that's literally the proof

[surreal sapphire]

is there a proof that is not by diagonalization?
yes proceeds to give proof by diagaonlization

[fervent pebble]

that's diagonalization mf

[sleek wing]

wait I thought you said by diagonalisation

oh well

here's what we're gonna do instead

we're gonna do it again but pick the diagonal off set by 1

[fervent pebble]

[sleek wing]

now it is not the main diagonal so I win you lose bye bye

lemme see if I can map the diagonal proof into some awful field extension meme

[surreal sapphire]

anyways, cantors diagonalization arguments are so fundamental and intrinsic to this, i dont think its possible

its also super low tech, so 🤷

show |P(X)| > |X| and then |P(N)| = |R|

[sleek wing]

maybe

nah

was thinking about using a completion meme

[surreal sapphire]

assume R is countable, then you get R from Q after adjoining countably many elements ...

[sleek wing]

yur

problem is I can't just assume that any root of a transcendental is transcendental

or I could just Q(pi, pi^1/2, pi^1/3, ...)

[sick burrow]

Just note from the construction of the real numbers that R is uncountable

[fervent pebble]

gamma pls

[sick burrow]

No like actually

[fervent pebble]

how

[sick burrow]

It's defined as sequences in Q

[neat frost]

That’s usually how you prove it no?

[sick burrow]

Sorta

A quotient of that at least

[fervent pebble]

o wait idk cauchy construction

i only know dedekind construction

[neat frost]

Actually no that’s not how we did it

Oh wait I’m thinking of something else lol whoops

[deep mango]

There's a nice proof that perfect nonempty metric spaces are uncountable

I dont think it's diagonalization?

I dont remember

[summer sandal]

Let $P$ be a perfect subset of $R^k$ and suppose $P = {x_1,...,x_n}$ is countable. Construct a sequence of neighborhhoods $V_n$ such that closure of $V_{n+1}$ is contained in $V_n$, $x_n$ is not in $V_{n+1}$. We have closure of $V_{n}$ is closed and bounded hence compact. The intersection of all the closure of $V_{n}$ is non-empty. This is how I vaguely remember it.

[storm sage]

michael penn has a video on this

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

It's sorta like a type of diagonalization but it uses the nested interval property

[summer sandal]

I forgot how we got the contradiction from this.

I think proving the intersection would be empty is how its done, so I misspoke.

[fathom swallow]

BenJr

[summer sandal]

there we go.

[deep mango]

Interesting

[ripe wasp]

anyone know some online classes or something similar to aops but for higher math?

the problem is that their range of classes ends at competition math, single variable calc and group theory

i wanna take classes like real analysis and topology

[fervent pebble]

mit ocw is probably the closest you'll get

there might be isolated lectures on yt too

[ripe wasp]

but a lot of the classes online r only for university students enrolled in the program or aren’t online or i don’t have the formal prerequisites for as in i haven’t taken the class for it yet but i may have self studied it

[ripe wasp]

i’m kind of looking for

like actual online classes

[fervent pebble]

yeah i really doubt there's anything like that but maybe someone else knows something?

sorry

[grizzled grove]

I wish someone help me understand hecke L functions and Artin L functions

[storm sage]

yeah the most there is are just online video series I think

maybe try coursera? @ripe wasp not sure if they have what you're looking for or not

or edX

[azure nymph]

Yeah you probably won't find much on an actual real analysis course online. Maybe try to find or start a group for that though?

[wicked ore]

@stiff aurora ok let’s say I’m alive

[stiff aurora]

@wicked ore
A = "your dead'
B = 'i will you money"
I promise if your dead, i will give you money
If A is false, then either I gave you money or not. Either way i've kept the promise

here we go

[wicked ore]

No no let’s say I’m alive

[stiff aurora]

yes your alive

[wicked ore]

Why does that mean your statement is true? Why isn’t it “undecided”?

[stiff aurora]

i gave you money, have i broken the promise?

[wicked ore]

No, but you haven’t proven you’re honest either

It’s just undecided

[stiff aurora]

all that matters is whether i've broken the promise or not

if i don't give you money, i haven't broken the promise either.

breaking or not is true or false

sure if you were working in a different system where undecided was an option then it'd be different

[wicked ore]

But this feels weird. If I tell you “hey I’ll pay you back once you die”, and you’re alive right now, logically that means my promise is good. But you wouldn’t believe me in real life!

[stiff aurora]

you've got to be careful with your wording

"i promise if your dead, then i will give you money"

it's logic so you have to be precise

[wicked ore]

Oh I see “if” rather than “when”

[stiff aurora]

you can think of it like a contract
you can't have imprecision in your contract cuz that'd make problems

[wicked ore]

If you’re not dead right now at this very second, then there’s no way to verify I was lying, which kinda means it was valid

[wicked ore]

But why isn’t undecided an option

[stiff aurora]

it's just the type of logic you/we chose

we decided to go with true/false

but your totally allowed to go true/false/undecided

but that would be a different logic which probably isnt the one ur studying

[wicked ore]

I see

[sick root]

Hi

[shrewd ocean]

hello

what's up with xournal++ on windows? it runs pretty normally for me so far

[neat lintel]

elaborate

[shrewd ocean]

a person mentioned that the software is scuffed on windows, but it works pretty fine to me

[sick burrow]

why did virustotal flag geogebra

with only one scanner granted

[limber thunder]

it works decent I guess

the dev team cares about fixing bugs and is still releasing new vers.

(that said, I use the linux build so I can't say much)

[ancient flame]

the epitome of the help channels

[toxic gale]

I mean, kudos to them, at least they didn't make people waste their time answering when they already know the answer.

[charred mortar]

Yeah maybe they just had an epiphany

[ancient flame]

ik but still funny

[toxic gale]

Oh wait I didn't realise it was the same person. OK yeah that's pretty funny.

[storm sage]

Hey that's me

[velvet dagger]

Actually that's your alt

[ancient flame]

damn

im so sad that technoblade died

:/

[wooden flax]

WHAT THE FUCK

@ancient flame bro i thoguht you were trolling

i just googled it

i love technoblade

ive been watching him for years

holy shit this is terrible

like what the f

[velvet dagger]

Yeah a few people mentioned it in another channel

Idk who that guy is but F nonetheless

[wooden flax]

bruh hes a legend

nah like you've got to watch one of his videos

he has that kind of humor which is funny and makes you wonder how he hasnt been cancelled

[velvet dagger]

"Makes you wonder how he hasn't been cancelled" sounds like it has potential to be....... concerning

[errant merlin]

techno's humor isn't problematic right?

been a while since i've watched him

[wooden flax]

no not like that

idk how to explain it

[ancient flame]

I wish

no he's different

longbeachgriffy is someone who somehow isn't canceled

techno's humor was (damn it's so sad to type was) not at all like that

sometimes he made some sketchy jokes

like orphan kids etc

but they're ridiculously funny

[wooden flax]

yeah thats what i meant

[ancient flame]

I love longbeachgriffy too tho lmao

[clear parcel]

Someone told me that if I got a PhD I would lose it if I did not continue to do research after earning it? What is the basis for this statement?

[neat lintel]

there is none

[clear parcel]

Ok thanks

[surreal sapphire]

you only lose it if you make a silly mistake on discord and someone corrects you
whoever does that gets to take your phd

[cinder sleet]

Like racing for pink slips

Play for keeps

Be a bad day to fat-finger the keyboard lol

[surreal sapphire]

what

[bright hill]

...

wtf

[ancient flame]

:/

wish I was joking

[bright hill]

But I thought he was doing well

Didn't his surgery work or whatever?

[ancient flame]

yep

he was doing well for a period of time

even uploaded a VR video 2 months ago

but I guess things took a turn for the worst

watch the latest video if you haven't already

[sleek wing]

No It’ll make me sadder sad

the saddest

[ancient flame]

I know but still

it's informative

[sleek wing]

I’ll watch it at some point

[ancient flame]

it's made by his dad

[cinder sleet]

Racing for pinks? Its when street racing cars the winner keeps the losers title to the car. The "pink slip"

[ancient flame]

I had a dream that they released another video a day later lol

[bright hill]

That was 6 months ago :(

[bright hill]

I did

[ancient flame]

no, 2 months ago

[bright hill]

I was lagging

[ancient flame]

oh lol

[bright hill]

That was supposed to be after this

[ancient flame]

ohhhh

[bright hill]

I can believe he apologized for selling out a lot the past year

Like

He's dead and that's what he's worried about

This is so unfair

[ancient flame]

well he's selfless

but yeah im sure he needed the money for treatment

[neat frost]

Good morning DarQ!

MODDY

HI

ILY

[sleek wing]

Jesse we need to sell merch

[neat frost]

WEW

[sleek wing]

Slurp.......

[neat frost]

WEW!!!!!!!!!!

[ancient flame]

WEW

ALORPY

ALORPY

FUCK

SLORPY

YAY

[neat frost]

NODDY

YAY

[ancient flame]

NODDY?

[neat frost]

MODDY

YOHAN

[ancient flame]

hello

[neat frost]

Bruhan

[rotund estuary]

Darn it

[sleek wing]

Bhutan

[rotund estuary]

I gotta deal with the VA again

Theyre so slow

[cinder sleet]

Veterans administration?

[rotund estuary]

Yeah

[cinder sleet]

Yup.. Me too

[rotund estuary]

Veterans affairs rather

[cinder sleet]

What u dealin with

[rotund estuary]

My stipend from the GI bill hasnt come in for this month yet

[cinder sleet]

Oh shit

[rotund estuary]

Yeah, it's no bueno

[cinder sleet]

U get disability or no

[rotund estuary]

No, just the gi bill

[cinder sleet]

Its even harder now... So many automated lines

[rotund estuary]

Yeah they really dont want people contacting them

[cinder sleet]

Ya... Its lame

Been down that road

By this month u mean june?

[rotund estuary]

July i think, i usually get my payments on the last few days of the month before

But at the end of june, no payment had come in

[cinder sleet]

Hmmm

Give it a day?

I wish u the best brother

[rotund estuary]

Thanks, hopefully it comes in

[bright hill]

It really isn't a good morning

But good morning nonetheless

[sick root]

Hi

[neat lintel]

anybody here attended a math workshop? what is it like? its my first time and I'm anxious

[neat frost]

Why are you nervous?

[neat lintel]

Im a noob, idk what I will be able to do there

[neat frost]

What exactly is a math workshop?

[neat lintel]

it's a week long workshop on graph theory and combinatorics, main focus being on collaboration

solving open problems

[neat frost]

Oh

Weird

[neat lintel]

my professor invited me (as a top student of graph theory), its going to be held in a hotel in some nice place in nature

[neat frost]

Oh nice!

[neat lintel]

he said it's okay if I don't contribute anything, but usually some progress is made by students

[charred mortar]

sounds like fun really

I wouldn't worry about progress myself tbh

[fervent pebble]

sup slurp, ab

[charred mortar]

hallo

[neat frost]

Heya valley

[charred mortar]

also make sure to steal all the hotel amenities

[neat lintel]

well what I want is all the sweet knowledge I can get from there ppl, but don't wanna be a useless figure there lol

[charred mortar]

honestly if you just learned a bunch of stuff I'd call that a success

[neat frost]

Sweet knowledge

You’ll do fine don’t sweat it

[charred mortar]

yeah

[neat frost]

And in any case you’ll get free food, so it shouldn’t really matter

[charred mortar]

free food makes it all worth

[neat lintel]

lol

would be nice to put that food expense to some use too tho

so they will invite me again

or like, they will want to collaborate with me again

[valid moat]

Ok so I have an idea that I'd like to get feedback on, which is actually why I joined this server. The idea is for a game like chess, but actually based upon the rules of mathematics, and as math is a constantly evolving discipline, would not be a solved game where you basically can't win against a good chess ai. It would be designed to be online in a server that has archives of the legal moves etc. and controlled by a rules committee who approve the addition of peer review proven moves and actions to the game's rules database. I'll be posting all the rules in just a second, and I'd like feedback as well as suggestions for new rules, actions etc.

Fermat: A Game For Math Nuts

[velvet dagger]

Uh

This feels like the kind of thing that would be veeeeery long

Can you write this into like, idk some online doc, send a mod a link

And if we'll tell you if/where it's appropriate to post?

[valid moat]

Sure

The rule set is extremely basic rn, which is why I'm looking for feedback, so it shouldn't be more than like 5 pages long

[velvet dagger]

more than 5 pa...

[charred mortar]

Yeah that’s huge for a discord channel

[velvet dagger]

Yeah definitely please do not post that in the actual text of any channel here lmfao

[valid moat]

Yeah I won't

[charred mortar]

I could barely be arsed to read five paragraphs tbh in a channel

[compact tartan]

you only need like a page of rules to do math

one of these

that's a very "raw" way to look at it though, but it has been tried before in e.g. metamath

e.g. http://us.metamath.org/mm_100.html

[valid moat]

True, but the idea is to give someone a puncher's chance through the possibility of a particularly creative solution or series of solutions. The increased complexity of the game also means computing power won't be as easily applied, even if its still possible

Of course something like Deep Blue will probably have a 99% Winrate, but at least its not 100%

perhaps, although its also designed to not be as solvable by humans, and in a way that it never ends in a draw, to make it more interesting. Plus its just a new take on a strategy game with a ruleset thats constantly evolving and getting more complex, so it will never be stagnant

Thanks

[compact tartan]

the problem is that math doesn't have a win condition

[static loom]

oh yeah prove it 😼

[valid moat]

The game has non math rules, like you can capture pieces and it ends when one player is out of pieces etc. Anyways I just sent it to an admin to review so hopefully you'll all get to read the doc soon

[deep nebula]

I see no hope for me. Studying for ap calc and ap chem and I got a month left. I am so dead

[silver hawk]

Haven’t the AP tests alrdy occurred?

[deep nebula]

for next year

[bright hill]

Ah yes

We got a month left for next year

[jade shore]

Phew

[static loom]

i wonder if he ever had something named after him, like a type of meal probably

ah, well I feel sorry for him that they named him after a programming language

[hollow sundial]

TIL. This is awesome.

[viscid pecan]

So wait this guy studied math and made some damn good curry too?

[full isle]

It comes up in abstract contexts in math

A nice example I can think of is when you define tangent plane of smooth manifolds as space of all derivations at a point

[neat lintel]

how so?

[storm sage]

LOL

[storm sage]

^

The easiest example of currying I can think of is if you switch from thinking of + as a function from (R, R) → R to instead a function from R → (R → R)

e.g. + takes in the number 6 and outputs the function +6 (add six)

[bronze pelican]

Oh so thats what thats called

This is happens a lot in mathematics

Object-action duality: when u view elements of a group simultaneously as elements of a set and transformations acting on sets

[bronze pelican]

Oh this is nice too, u view a tangent vector (object) as a derivation (action)

[analog salmon]

My dad was an undergraduate math major at Yale, and he was telling me some cool stories and showing me his old papers

His senior advisor was Benoit B. Mandelbrot, and one advising session, Mandelbrot gave him two papers to read before their next meeting

My dad left, looked at the papers, and found out that one of them was written entirely in French. Which he didn't know at all.

Another cool story, he had Serge Lang for abstract algebra, and the notes that Lang passed out where drafts of his undergraduate algebra book

He also did awful in that class, got a 5/100 on one test and 15/100 on another. Some of his answers just had "nonsense" written in red sharpie by Lang

Also had a bunch of printouts of some of Lang's more political published (and unpublished) works

things like "rats in a box", or an ad he took out from a journal because said journal wouldn't publish his article about higher education

[vivid halo]

Serge Lang's more political works

[peak tide]

then there's the classic story wherein serge lang was temporarily using ken ribet's office while he was away, and opened ribet's copy of lang's algebra, and found that ribet had written "pretentious ass" below the preface. lang wrote a reply:

also, apparently he often threw chalk at students 😆

[deep mango]

I actually had ken ribet as an algebra prof (for about 2 days before I gave up and took a different class) and he talked about this at the start since he was using lang's book

@supple flame

Yes

He likes lang

[neat lintel]

Is the square root of irrational number irrational

Always

[errant merlin]

a rational number squared is always rational

[proud olive]

That's a neat proof

[neat lintel]

not done yet

prove : a rational number squared is always rational

[neat lintel]

Had to read this the second time lmao

[trail sundial]

I’m awful with rigorous proofs by this seems pretty easy

Do I have to prove that an integer squared is always an integer?

[proud olive]

That u can do urself

[neat lintel]

I have lmao

[neat lintel]

yes sir

or atleast ur learning isn't complete

if u can't do it

[neat lintel]

Let a rational number be p/q
Then (p/q)² = p²/q²

If p is an integer, then p² is p.p is also an integer, since the integers form a magma under multiplication, so is q²
Hence p²/q² is a rational number

actually how do u do it

[trail sundial]

Distribute the exponent to the numerator and denominator. An integer squared is always an integer. Done

[neat lintel]

oh mb

I solved a different problem

somehow

I wanted to generalize this to all natural exponents

it's still the same logic

Yep

interesting

[maiden bear]

it's all addition

[neat lintel]

this looks interesting prove

$x^2 \in \mathbb{N}$ if $x \in \mathbb{N}$

[fathom swallow]

∆y/∆x=πy+π^2x

[neat lintel]

without

using

the fact that

product of two integers

give another integer

[proud olive]

I have no idea how you're supposed to prove that on a more fundamental level

[maiden bear]

i mean

take n^2

thats n*n

and what's n*n

buncha addition

[proud olive]

That's going to be some Mathematica principa

[surreal sapphire]

you prove this how you prove every fact about the natural numbers

its just induction

[neat lintel]

sum of integers is integer prove that as well

[maiden bear]

induction

[neat lintel]

[maiden bear]

[proud olive]

Oh

[surreal sapphire]

its all just induction

nothing interesting happening here

[proud olive]

Always has been

[maiden bear]

follows from construction over the successor function

[neat lintel]

I haven't done any induction

[maiden bear]

it's really all induction

[proud olive]

Heck!

[neat lintel]

ok u right

[proud olive]

shoots astronaut

[neat lintel]

shoots again

wait

does bullets

even work

in space

[proud olive]

Gunpowder doesn't need oxygen to react

[maiden bear]

you need oxygen

for ignition

what

it doesn't?

[neat lintel]

how can combustion occur with no O2

[proud olive]

Nop

[maiden bear]

no hes right

i just googled it

[proud olive]

No clue

Ain't no chemist

[maiden bear]

Apparently its roughly like

they don't need oxygen from outer influences

[proud olive]

Gah bad mood today

[maiden bear]

because somehow the molecules contain some

[proud olive]

Bad internet connection too

[neat lintel]

molecules already contain O2 Or something?

so it's plausible

[neat lintel]

Let x = 1

1ⁿ = 1 (natural number), where n is any natural number.
Assume it holds for xⁿ
It must hold for x^(n+1) too
x^(n+1) = xⁿ.x
Since xⁿ is a natural number
xⁿ.x = q where q is a natural number, since natural numbers are closed under multiplication:
Let there be two natural numbers a and b
a.b = a+a+a+a+...+a (b times), and natural numbers are closed under addition, hence they are closed under multiplication
Hence xⁿ is also a natural number
Our assumption is true, and it holds that x^(n+1) is also a natural number.
Hence xⁿ is always a natural number for natural number n by induction

[neat lintel]

ya

[neat lintel]

what do u mean by closed??

Closure property

[proud olive]

Whoa that's a lot of words

[neat lintel]

Yea

[proud olive]

Too bad im not reading them

[neat lintel]

whats that lol

I can't seem to simplify it down

[neat lintel]

If a and b belong to set A, and if a+b also belongs to set A, then the operation + is closed for all elements in A

[proud olive]

Closed during addition

[neat lintel]

Under
Yea

[neat lintel]

ooo

[proud olive]

*under

[neat lintel]

[surreal sapphire]

ah yes, assume natural numbers are closed with respect to multiplication, then they are closed with respect to multiplication

[maiden bear]

ye was thinking the same

multiplication is just addition in disguise, you assumed the thing you were trying to prove

[neat lintel]

explain

how

0.1*0.1

[neat lintel]

ah yess lol

is addition in disguise

or

sqrt(2) * sqrt(3)

[proud olive]

U add it 0.1 times

[neat lintel]

what does that mean

[proud olive]

Ur welcome

[maiden bear]

almost as if we were talking about natural numbers

[proud olive]

Wasn't aware of that

Didnt read the thing

[neat lintel]

ok then what about irrationals

[maiden bear]

my brother in christ

are those natural numbers

[surreal sapphire]

$m\cdot n$ is defined as
$$m\cdot n \coloneqq \begin{cases} m\cdot(n-1)+n &\text{if $n > 1$} \ m &\text{if $n=1$}\end{cases}$$

[fathom swallow]

Lochverstärker

[neat lintel]

u are only talking about naturals?

[surreal sapphire]

so if you recursively apply this, its just addition

[maiden bear]

did we talk about anything else

the last 10 mins

[neat lintel]

yes

guns

[surreal sapphire]

so at the end of the day this comes down to showing that the sum of two natural numbers is a natural number

[proud olive]

How do u read and react so darn quickly @maiden bear ?

[maiden bear]

with my eyes preferably

[proud olive]

Booo

[neat lintel]

he has chip implanted in hus brain lol

[neat lintel]

https://tenor.com/view/why-whatever-gif-23592041

[surreal sapphire]

and addition is defined as $$m+n \coloneqq \begin{cases} (m+(n-1)) + 1 &\text{if $n > 0$} \ m &\text{if $n=0$} \end{cases}$$

[maiden bear]

me

[proud olive]

mif

[fathom swallow]

Lochverstärker

[surreal sapphire]

where "+1" is always the successor function applied

now its clear from the definitions and the axioms (specifically on the successor function) that the sum of two natural numbers is a natural numbers

and then you can do induction to show that the sum of any (finite) number of natural number is a natural number

and hence the product of two natural numbers is a natural number

now ofc nobody does this, because this is obvious

and the natural numbers are set up in a way precisely to make this true

[maiden bear]

we take R and cut the commata

[maiden loom]

why

[surreal sapphire]

hm?

because it works

[nimble jetty]

Alright I'm trying to create a non-positional number system and need some help.
Instead of each place representing it's digit times a power of ten, I'm looking for something separate that has similar qualities. For example, Roman numerals.

I had one but it really fell apart

To be clear, I'm looking for something that isn't positional OR roman numerals

[stiff aurora]

i mean with base 1, you can make a lot of non-positional systems.

also: https://en.wikipedia.org/wiki/List_of_numeral_systems#Non-positional_notation

[fathom swallow]

Failed to get a response from Wolfram Alpha.
If the problem persists, please contact support.

Jul 3, 2022, 5:42 PM

Failed to get a response from Wolfram Alpha.
If the problem persists, please contact support.

Jul 3, 2022, 5:42 PM

Failed to get a response from Wolfram Alpha.
If the problem persists, please contact support.

Jul 3, 2022, 5:43 PM

[zenith tinsel]

closure is a neat concept

didn't know it was so important until I actually started using it in linear algebra now

me when addition $+: \bR \times \bR \to \bR$

[fathom swallow]

texaspb

[static loom]

trick (or maybe not) question for you, are the rationals closed under addition? because e=1/0!+1/1!+1/2!+... is a sum of only rational numbers

[storm sage]

😭

[placid quartz]

are naturals closed under addition? because 1+2+3+... = -1/12

[zenith tinsel]

idk how to answer

but if I were to guess the answer is no

[storm sage]

hint: ||rational numbers are not closed under limits||

[fervent pebble]

i feel like the answer is yes tbh

i would buy the rationals as closed under addition

[neat lintel]

[fervent pebble]

whattt

am i wrong?

[neat lintel]

you should know this beyond any reasonable doubt

[zenith tinsel]

wait

[fervent pebble]

texas said no so i got confused

[zenith tinsel]

wait

something is happening

i think ive got an idea

[neat lintel]

if you know, don't ruin the fun

[zenith tinsel]

ok so the rational numbers aren't closed under addition bc 1/x messes things up

idk

?

[fervent pebble]

wat

no they're closed under addition

[zenith tinsel]

like you can't 1/x

[fervent pebble]

im certain

[zenith tinsel]

if x = 0

[fervent pebble]

that's division

[zenith tinsel]

but 1/x is a rational number

is what i mean

[fervent pebble]

not if x = 0

[zenith tinsel]

ok im dumb

[static loom]

well you can't 1/x with x=0 in R either

[neat lintel]

what does division have to do with whether or not the rationals are closed under addition?

this is a good question mero, gonna steal it

i need to troll people

[zenith tinsel]

bc I thought that the fact of 1/x not being well defined for all x would make things messy

[cold needle]

this is a good troll

[fervent pebble]

[static loom]

haha well I think it's a kind of misconception I had when I was taking calculus and learned closure the first time too in abstract algebra for a bit

[cold needle]

i think i know why its a troll but 😵‍💫

i dont want to share

[static loom]

like good to think about and know confidently for sure lol

[neat lintel]

it's a little troll-y, but it's also very good

[fervent pebble]

say, what's the trick with the e-thing supposed to be?

[zenith tinsel]

what's the joke

[fervent pebble]

because if it was supposed to screw me over i didnt even understand what it was supposed to do lol

ohhh wait the argument would be that because a sequence of rationals can construct an irrational they wouldn't be closed?

[zenith tinsel]

ok so wait a minute

[fervent pebble]

o yeah if id thought abt that a bit more it would've tripped me up lol

[zenith tinsel]

if R is closed under addition

why wouldn't the rationals be too

[static loom]

the world would be a weird place if all limits of rational numbers was rational haha

[fervent pebble]

lets go tho 😎 didn't think abt it and got it correct

[neat lintel]

leading question: how would you write "the rationals are closed under addition" in math symbols?

stop giving away the answer

[storm sage]

😭

[zenith tinsel]

$\bQ \subset \bR$

[fathom swallow]

texaspb

[zenith tinsel]

😎

proof done

[storm sage]

that doesn't prove it

lol

[fervent pebble]

$\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}$?

[storm sage]

{1,2} is a subset of R

{1,2} is not closed under addition

[neat lintel]

c/d

[fervent pebble]

i meant d under the c yes

there

[fathom swallow]

13 x 7 = 91

[zenith tinsel]

$ad + cb \in \bZ$

[fathom swallow]

texaspb

[zenith tinsel]

$bd \in \bZ$

[storm sage]

oh cool, ,didn't know \bZ was a thing

I've been doing \mathbb{Z} this whole time 😭

[fathom swallow]

texaspb

[fervent pebble]

there's \bR \bC and \bQ too

[storm sage]

that's so good

[fervent pebble]

i think maybe \bP too for primes

[storm sage]

is there \bF

[fervent pebble]

$\bF$

[storm sage]

actually I can just test it nvm

[fathom swallow]

13 x 7 = 91
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[storm sage]

lol rip

okay but that's still cool

what package is that

[fervent pebble]

$\bC \bQ \bR \bP$

[fathom swallow]

13 x 7 = 91
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fervent pebble]

huh no bP rip

[zenith tinsel]

def of rational number is for $p, q \in \bZ$, $\frac{p}{q} \in \bQ$

[fathom swallow]

texaspb

[zenith tinsel]

right

[fervent pebble]

yeah

[zenith tinsel]

ok

[fervent pebble]

iirc

well

once division is defined

or multiplication by reciprocal

[neat lintel]

so if a/b and c/d are rational numbers, is their sum?

[fervent pebble]

yes

[neat lintel]

there you go

[zenith tinsel]

so addition of rational numbers would be $\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}$

[fervent pebble]

!

[fathom swallow]

texaspb

[zenith tinsel]

so if the numerator and the denominator evaluate to an integer

do we have a rational number

[neat lintel]

you posted the definition of a rational number above, what do you think?

[zenith tinsel]

yes

[fervent pebble]

yes by def of rational

[zenith tinsel]

yes

ok so

the rationals are closed under addition

by definition

[fervent pebble]

yep

and subtraction

and multiplication, i think

not division tho

[zenith tinsel]

$\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}$

[fathom swallow]

texaspb

[zenith tinsel]

cool

so the question was just a little trolling

[storm sage]

but why

what doesn't work?

[fervent pebble]

0

[neat lintel]

[fervent pebble]

you can't divide by 0

and 0 is rational

[neat lintel]

maybe you can't

[fervent pebble]

i forgot some ppl are just built diff

[zenith tinsel]

so $0 \in \bQ$

[fathom swallow]

texaspb

[zenith tinsel]

idk why but that's cool too

[storm sage]

that is pretty cool

also it's actually a nice exercise to figure out a good definition of the rational numbers

it's harder than it might first seem

[zenith tinsel]

?

a good definition meaning

you mean like instead of having integers as the denominator and numerator, we have any real number?

[storm sage]

no like

[storm sage]

for example this definition doesn't work out too well because we haven't defined what division is

[zenith tinsel]

isn't that definition just a representation tho?

[fervent pebble]

define reciprocals and multiplication instead

and call it a day

[storm sage]

yes, but just using that definition alone, I have no way of knowing for example that 1/2 = 2/4

[zenith tinsel]

oh right

[storm sage]

so you need a little bit more machinery

it's nice to think about

really gets your mathematical gears turning lol

and then, there's the beast that is defining the real numbers using the rational numbers

and that is much harder conceptually

[fervent pebble]

idek how ppl came up with dedekind cuts

[storm sage]

The logic is that dedekind cuts are kind of analogous to a limit

like if you want to define the square root of two, you take the set of all rationals q such that q^2 = 2

and then that gets you arbitrarily close to sqrt(2) but never quite equal

It's so fascinating

[fervent pebble]

and then you define the cut instead as the real number

it's so clever

[ancient flame]

you also don't need the curly brackets for one-character inputs

e.g. $\mathbb Z$ or $\frac a b$

[fathom swallow]

gmod

[storm sage]

well yea but you need something to separate the command from the letter anyways so I don't mind

[ancient flame]

true

[storm sage]

you're right tho

[ancient flame]

on mobile it's kind of a hassle to do curly brackets

[storm sage]

yea that's true

I'm on a laptop tho so the difference is p slim

[ancient flame]

yeah

[storm sage]

also I can't tell you how many times I've looked up a latex error and the solution is just to add more curly braces

😭

[ancient flame]

it also allows me to make my latex as compact and unreadable as possible

lmao

[storm sage]

goalsss

[ancient flame]

LOO

LOL

[zenith tinsel]

$\sqrt a$

[fathom swallow]

texaspb

[zenith tinsel]

that's so useful omg thx

$\sqrt a + b + c$

[fathom swallow]

texaspb

[storm sage]

yeah the { } is just for grouping

shortcuts are always nice tho :)

[tender tulip]

if (G,*) , is the generating subgroup, H, of a subset A of G the "smallest" group such that
AH = HA = H considering product of subsets of a group

[neat lintel]

#❓how-to-get-help

[tender tulip]

literally it's a yes or no

kinda not able to work it out rn

[ancient flame]

LMAO fucking minimods

[storm sage]

what is the question..?

[zenith tinsel]

if $(G,*)$ is the generating subgroup, $H$ of $A \subset G$ the "smallest" group such that $AH = HA = H$ considering product of subsets of a group.

[fathom swallow]

texaspb

[zenith tinsel]

holy shit I didn't understand jack

this is so poorly phrased

[storm sage]

yeah I'm a bit confused

but tbh

phrasing the question in math is half the struggle

[neat lintel]

it shouldn't be a struggle

[storm sage]

It is a struggle

[dark sable]

From discussion channel 1 I have this quetion: Converting all math to binary wouldn't be more easy its more simple, why do we still do math with a 10 base numerical system?

[fervent pebble]

we've been using base ten for thousands of years now

it's just too hard to switch everything, not even considering whether it would be worth it or not

[neat lintel]

ten fingers

ten toes

[dark sable]

Sure, I agree with you, but maybe we discover new math under binary system

[dark sable]

Oh I planned wrongly the question, why do we still use...

[fervent pebble]

the base of the number system doesn't actually matter

it doesn't actually change any significant properties

[dark sable]

I know, but maybe aspects that seems complex are simpler than we spected

[fervent pebble]

the only thing that happens is that some decimal expansions show patterns they might not otherwise

eh, if you really think so then be the change you wish to see and give it a shot

who knows? you might actually find something neat

i wouldn't get your hopes up, though

[dark sable]

I'll try it

[azure nymph]

I think base-2 would make everything much longer, I am also unsure how decimals works in base-2

[storm sage]

the number 986 you can express in three digits in base ten, how many digits do you need in base two?

base two makes numbers a lot longer

base 12 on the other hand.. that's where it's at

or base 24

[swift sinew]

While you're at it, just use base n!

[zenith tinsel]

wait a minute

[zenith tinsel]

can you even define that?

😮

how would that work

[kind horizon]

in the same way we use quaternions to represent rotations in 3 dimensions

can we use spheres to represent 2d rotations

can we generalize this?

[storm sage]

we use complex numbers on the unit circle to represent 2d rotations

[kind horizon]

take a space of n dimensions, then we can represent a rotation in its hyperspace along some spherical object in the n dimension

[kind horizon]

i see

[storm sage]

for example rotating by 90 degrees counterclockwise is analogous to multiplication by i

[swift sinew]

Here's a nice exposition on the topic of rotations in higher dimensions:
https://www.euclideanspace.com/maths/geometry/rotations/theory/nDimensions/index.htm

[tender tulip]

For some group (G,*)
and given some subset A, is <A> = (H,*) the "smallest" (under subset inclusion) subset of G such that
AH = HA = A and AA = A [indempotent] when considering subset product

aka for subset X and subset Y, XY is the set of elements xy where x in X and y in Y

[vivid halo]

Use base e, it’s the most efficient

[velvet dagger]

Base identity?

[ancient flame]

momg so fmunni

[neat lintel]

True

[ancient flame]

happy 4th motherfuckers

[bright hill]

Oh shit

@neat frost happy birthday

🥳

[ancient flame]

@neat frost HAPPY BIRTHDAY

[neat frost]

Thank you! Don’t forget tomorrow as well!

[neat frost]

Fank you moddy!

[ancient flame]

ily <3

oh right

#chill

[neat lintel]

fank u or thank u

[zenith tinsel]

happy birthday #chill

oh fuck this isn't chill

shit

now I sound like a schizo

[steep compass]

nah we all talk to ourselves from time to time

yes that's right :3

ure so cool Empress

ty Empress

ugh now we sound like someone with a large ego

but, ure the Empress u deserve it

yea yea

uhmm we shouldn't talk here

well don't see general chat around

well ure right ig

food?

https://tenor.com/view/mexican-cuisine-mexican-food-yummy-food-gif-17915340

yess i love taco's

u do me2

less be friends forever :3

taco taco

we love taco

wait did the channel just move?

who cares

know what should be cared about?

bunnies?

yes and mental health

to many dying from suicide

😒 ure thinking about him again aren't cha

u know he doesn't give a crap about u

only his bf luca

stop chasing and carrying so much about a guy that doesn't even want u in his life

🥺 i know i know but, we been friends for a long time

listen ure way better of focusing new people who actually care about u

but, but no one ever does

[stable ginkgo]

😃

[steep compass]

that's not true ure panic thinking again

look u found someone u loved u can do again

and this time they will love u back

don't worry

but, it won't be like him people just don't care these days >.<

not everyone is the same

i know people are selfish and quite hypcrotical

but, that isn't the end of it

😒 yea right tell that to urself

well i am talking to myself 😐 ...

we do this quite often

in fact

...

always have to correct urself

are we going to ignore that person with the emoticon?

[steep compass]

that one?

they just got attention didn't they

yea i guess your right

say say

did u watch Next the tv show

it was quite good right?

it was watchable i agree

could been better the old fart got quite boring

not a single char i like so far

oh common do u always have to be so critising?

cant u just enjoy the show

😁 come come it's fun right?

sigh

why ure always so tiresome?

it's called being emotional and yes i have them

i call it bothersome..

[zenith tinsel]

oh my God

[steep compass]

how do we agree even so many times

[zenith tinsel]

who are you talking to

[steep compass]

myself?

whoa that was disrespectful

shuddap

there's no need to get emotionally

he's just a normal guy wondering wtf going on

try and be a bit, more nice would ya

[zenith tinsel]

nice

[steep compass]

but, sen...

[zenith tinsel]

that looks like some lyrics to a song

for some reason

[steep compass]

he does have a point

well we do love to write lycrish

music is the sound of the soul

TIMR WASTE

if u where to ask me

we are better of learning something usefule

flying from the sky

watch me burn it down

oh dear no

[zenith tinsel]

😭 I don't understand what you're talking about

[steep compass]

who?

me

or me 😄

[zenith tinsel]

😭

[steep compass]

no no didn't mean to make u cry 😦

ugh are u seriouse?

[steep compass]

want a hug?

shut up

ure embaricing me...

but i like making new friends 😦

no 😒

[zenith tinsel]

oh I got it

you're playing the schizo

[steep compass]

yep didn't want to make u feel alone here 😦

talking to oneself can be perfectly normal

useful even

when going over problems 😄

although that just imagination and not, actually voices

now what?

i dunno

talking to myself is actually kinda comftrable

say wanna talk about

yep :3

https://tenor.com/view/yuukoku-no-moriarty-moriarty-the-patriot-william-james-moriarty-william-moriarty-moriarty-gif-22040043

[zenith tinsel]

I think you're probably getting muted

bc of spam

but idk

[steep compass]

maybe

[zenith tinsel]

so apparently

you roleplay as this character in your pfp right

[steep compass]

yep

[zenith tinsel]

gotcha

where is it from

[steep compass]

Kill la Kill

she looks like rainbow lady gagag

[zenith tinsel]

interesting

[steep compass]

but don't let that fool u

[zenith tinsel]

she's got big booba

[steep compass]

u should see her in her ultimate outfit

[zenith tinsel]

nice honking chonkers

[bright hill]

but july 4th is your canonical birthday, isn't it?

[steep compass]

the anime is basically the less clothes the stronger they become

[bright hill]

I think I gave you all the happy birthdays I needed

[steep compass]

pats

[bright hill]

[steep compass]

scratches ear

such a good kitty

[bright hill]

[steep compass]

uses laser pointer

[neat frost]

Not quite

Almost there

[steep compass]

oh wait ure a red raccoon panda bear

[neat lintel]

their dangerous aren't they?

[steep compass]

yep very danger

much floof

[neat lintel]

i need someone to answer my quick questions pls

if they don't mind

im forgetful

#help-0

so ya uwu help me pls

what is divided by what in a Frequency table in order to get the mean
ik u have to divide by total frequency
tho wut value do u have to divide
anyone mind answering pls?
also wuts the formula for area of a circle

[steep compass]

Pi r^2
For area if the circle.

[bright hill]

nice try

[glad grove]

Yall,, what if there was a Mathematics discord server project where people went onto Wikibooks and helped fill in the math knowledge on their open-source books?
Like,,, It would significantly benefit that community if people just started making those projects more extensive
And it would increase access to knowledge for all
There's headway in these books and they could be good starters

[zenith tinsel]

what website is that?

that's very nice

[storm sage]

That'd be pretty cool

I could def help with some of those topics

[bronze pelican]

U could contribute to Wikipedia

Oh interesting

[neat lintel]

Can I start analysis without calc 3 and linear algebra

[bronze pelican]

Lmao there's a "solutions to hartshorne" wikibook

[storm sage]

LOL

[storm sage]

Yes

[neat lintel]

I keep getting board

And not finishing the things I try to self study

[storm sage]

nooo finish one thing first

[neat lintel]

I am a quarter through linear lalgebra

In kahn academy

I have a very hard time with concentration

I want to do whatever I am not doing

[azure nymph]

Do you have a goal for studying?

[viscid pecan]

I’d do Linear Algebra first

[neat lintel]

I want to get an internship

[spring crypt]

the other channel is being used for a (interesting imo) discussion and I don't want to interrupt it because I'm just going to be venting a bit anyway

so my master's thesis is submitted and the defence is approaching

and I'm so fucking terrified

I have spent a week trying to begin preparing the defence and I haven't managed to do a single thing for that until today because I'm kinda paralysed by fear or something like that

it's weird

and bad

[storm sage]

Damn :/

I get that feeling, defences sound so scary

How long have you been working on the thesis for

[abstract pilot]

Anyone here use Wolfram Cloud for mathematica?

[spring crypt]

Since september, and solely focusing on it since like january

[storm sage]

What's it about

Out of curiosity

Also if you don't want to vent in public, my DMs are open if you want

[spring crypt]

whining in public is fine but thanks lmao

just stressed out but yeah

here is the abstract

going to bed now it's like 1 am here lol

but tomorrow feel free to ping me if you want me to explain something about that 🙂

bye and thanks for listening to me vent 😄

[storm sage]

yeah of course good night I wish you the best of luck

[glad grove]

I've focused on Abstract Algebra, Calculus, High School Mathematics Extensions, and I'm still looking around.

Maybe if it was promoted it could get some traction

[storm sage]

lemme know if there's some specific gruntwork you wanna get done lol

[glad grove]

You can, but it might be nice to look at how single-variable calc goes to calc 3 and how linear algebra sets up some of the theoretical aspects of analysis

[storm sage]

I can prob start my hand on an easy topic

[glad grove]

Not much rn I'm just sort of editing and adding wherever

[storm sage]

kk

[carmine creek]

linear algebra or calc first

[ancient flame]

@carmine creek what kind of calc

like first course on calc?

[carmine creek]

everything up to multivariable calc

[ancient flame]

calc first

[carmine creek]

oh ok

[velvet dagger]

LA should go before multi

Hard disagree with the alternative even though every fuckin undergrad in this godforsaken country does that

[ancient flame]

yes

[carmine creek]

thanks for ur advice :)

[velvet dagger]

LA and single variable in principle are switchable

[ancient flame]

yeah true

but I think calc is best to learn first

[storm sage]

linear algebra before multivar calc

definitely

[neat lintel]

LA can be utilized in cs

[storm sage]

although you won't learn all the stuff you need for multivar calc in a first semester linear algebra class (for example figuring out if a matrix is positive definite by finding the principal minors)

I would put linear algebra after single variable calculus so you have intuition with linear operators like differentiation and integration

[neat lintel]

linear maps are just matrices

differentiation and integration

[storm sage]

actually I think you mean linear maps between R-vector spaces are isomorphic to R-matrices as R-algebras under given bases for the vector spaces

[neat lintel]

they are matrices

[storm sage]

to be fair there is one important distinction which is that linear maps are basis-independent

whereas to find the matrix of a linear map you need to choose a basis

[neat lintel]

matrices

[storm sage]

we stan boxes of numbers

[rich moth]

how many digits of pi can you memorize

[storm sage]

I know at least pi

[rich moth]

i love fucking advertising on reddit

i dont get banned

🤡

[rose dock]

I mean you don't need to

[storm sage]

yea I mean you learn it in a multi course usually

[rich moth]

yoyoyoyoyo it's me questaor

[storm sage]

which sucks if you don't know anything about matrices and you frantically teach yourself matrix multiplication while trying to keep up on the multivariable content 😅

[azure nymph]

Did you really just add another M to your name

[rich moth]

how many digits of pi can you memorize

[azure nymph]

None it's useless

[rich moth]

no it'snot

you're training your memory

[full isle]

I dont know if this is possible

[mystic lintel]

Hey I had a question, should I do this chapter from my book or start integration, more differentiation and etc? I was thinking of leaving this for later but I just want some idea in what I should do

[terse flax]

I think you'll need integrals to do discrete probability

[mystic lintel]

I see

[mystic lintel]

So it would be better if i did these topics before doing that statistics one?

[wanton shoal]

I'm trying to find a fast way to compute rational solutions to a 2d quartic function for when it is equal to a rational number squared

basically I want to find when $\sqrt{\left(2xy\left(x-y\right)\right)^{2}+\left(x+y\right)^{2}}$ is rational for rational $x$ and $y$.

[fathom swallow]

Chixen

[wanton shoal]

what methods exist? I can't find anything online that I understand

[vivid halo]

you're essentially asking about rational points on plane quartics

[wanton shoal]

yeah

[vivid halo]

yeah this is very very hard in general

[wanton shoal]

ah

I figured

[vivid halo]

even for cubics this is like

not at all understood fully

[wanton shoal]

I've been trying to solve this one curve for a long time now

[vivid halo]

yeah for some curves you might be able to do this

but it depends on the curve

[wanton shoal]

this is the closest ive gotten because it started as some six degree 4d curve

[compact tartan]

actually, related (sorry for derailing)

nG what's your take on rational solutions to $\cos \pi a = \cos \pi b \cos \pi c$

[vivid halo]

what about it?

[compact tartan]

er

[fathom swallow]

mniip

[vivid halo]

hurb

idk can you write this as a polynomial lol

[wanton shoal]

I still would like to know if there is some way to find solutions, even if I still need to brute force with some equation

[compact tartan]

this is actually part of lie root system stuff and like dynkin diagrams

[vivid halo]

but yeah rational points on curves is very hard

[compact tartan]

I wonder if there's an elementary way to get it