serious-discussion

[stark charm]

o

[wild lantern]

Lol

[vast surge]

This was for whoever asked about differential galois theory by the way

[neat lintel]

yes (and as an unrelated note), it turns out that if a polynomial's derivative is irreducible in a field then the polynomial must be separable in said field

[wild lantern]

Do you have a reference or source you like for reading about differential galois theory?

[errant ridge]

damn differential algebra is so cool I wanna learn it so bad, but I need prereqs first

[vast surge]

Magid's lecture notes are good I think

[neat lintel]

there should be books too

I'm too busy with all the other math I'm doing, differential galois theory seems cool though

[neat lintel]

Hello, I would need someone who knows how to calculate the probabilities of winning or losing according to a percentage of success (I don't know if you understood me)

[maiden bear]

[surreal sapphire]

try reading #❓how-to-get-help first

[bronze pelican]

Who tf came up with this colorscheme for a textbook cover

[cyan goblet]

my beloved yellow books…

[fair mural]

yamin over here taking a picture of his computer screen

[empty stratus]

Maybe it's the version for red-green colorblind folks? xD

[neat lintel]

imagine reading algebra by lang on the first go

literal death

[austere timber]

;

;

[wooden flax]

differential galois theory is also very cool

i read a paper on it once

[vast surge]

What the fuck. This has to be edited in some way.

[primal seal]

That’s actually an incredible book

Reading it currently

Although that may be a bootleg color scheme

[bronze pelican]

I referenced it for exceptional aut of S_6

[sleek wing]

look. there he is. the man with the exceptional automorphism. I wonder what he's going to do this time. I sure hope it's not "mentioning the exceptional aut of S_6"

[fair estuary]

Guys, there's a math fight in help room 2. What do I do?

[open aspen]

bring snacks

start a betting pool

[deep mango]

In the future DM modmail or ping mods in the channel, i'll look at it now

[fair estuary]

Ok

[deep mango]

Ok this is not a fight

nevermind

Lol

[fair estuary]

They're fighting though

About math

[open aspen]

(dont bring snacks to actual fights)

that is generally considered bad taste

[deep mango]

Yeah you only need to ping mods if it's like, vitriolic. An argument is fine

[deep mango]

The snacks taste good

[fair estuary]

Is there a way to separate them into teams and then they can collaborate on their argument?

[deep mango]

Lol

[fair estuary]

It's too messy rn

[deep mango]

They will have to self-organize

[open aspen]

form unions

[cyan goblet]

better not be forming unions in my beautiful us of a

[fair estuary]

^Jeff Bezos

[broken compass]

Hello! I'm not sure if this is the right channel for this, but I was wondering, do you guys think finding the surface area of a bean might be a good Math Internal assessment HL topic? I took inspiration from looking for the surface area of an egg and thought it would be similar in difficulty, and thus, good for a Math IA topic for next year, I'd really appreciate any perspectives on this🙏

[open aspen]

I think so! You can attempt to generalize methods to other irregular surfaces as well if it turns out to be too simole

And this will give you some personal motivation points or however it's called

[azure nymph]

The yellow books look so good

[open aspen]

anyone else enjoy just scrolling through latex documentation trying to guess at what the crazy notations could represent

[fair mural]

i just wow at the cool symbols

[ancient flame]

lol

[sonic sentinel]

no

[azure nymph]

These are like unreadable

[untold sapphire]

dope

[limber perch]

my type of textbook

[torn willow]

So,How does a normal PDE textbook look like?

Random equation -followed by just lines and lines of derivation?

Like this for example

[stark charm]

yeah

pretty much

context and history for random equations

and then the rest

honestly its pretty aesthetic

[static loom]

sweet jesus

that textbook cover is actually genius, it forces you to open it so that you don't have to look at it, thereby encouraging you to study more

[leaden skiff]

@nocturne tusk so do u wanna learn abt induction?

[nocturne tusk]

idk what I wanna learn icl

I just wanna learn

something

[errant merlin]

induction is a must-learn

very useful

and also intuitive

[nocturne tusk]

I suppose so

[leaden skiff]

well like unless youre really interested theres no point in tryna learn it lol

[nocturne tusk]

sorry im having a big adhd moment rn

[leaden skiff]

if there is something specific you want help with let us know

[errant merlin]

Ah

You were originally trying to prove the power rule right?

And someone recommended induction

[nocturne tusk]

yes

[leaden skiff]

do you know the binomial theorem?

[nocturne tusk]

I know the basic stuff I think

[leaden skiff]

like, do u know how to expand $(a+b)^n$

[nocturne tusk]

like (3+x^-1)^7 or smth

[fathom swallow]

Ninja

[nocturne tusk]

I think so

yeah yeah

[leaden skiff]

do you want someone to help you prove it yourself or do you just want to see a proof of it?

[nocturne tusk]

proof for myself i think

[leaden skiff]

ok so, can you expand this for me? do you know the formula

[nocturne tusk]

idk the official notation but I cam get something

[leaden skiff]

yeah use whatever notation you want

[nocturne tusk]

$a^n+a^{n-1}\binom{n}{1}(b^1)+\cdots +a^0\binom{n}{n}(b^n)$

awful latex but I think its semi readable

[errant merlin]

Nice, that's correct

[nocturne tusk]

idk how to do column vectors lol

[leaden skiff]

column vectors?

oh you mean like in latex right, not for this problem

$^nC_r$

[fathom swallow]

Ninja

[errant merlin]

Ah

[surreal sapphire]

there is a $\binom{n}{k}$ command

[fathom swallow]

Lochverstärker

[nocturne tusk]

im gonna correct my thing just so it stops annoying me

[fathom swallow]

Ninja

$\mqty(x \\ y \\ z)$

[errant merlin]

Nice

[toxic gale]

Is that a built-in thing or your own shortcut?

[leaden skiff]

built in

[toxic gale]

💀

[errant merlin]

I've been using \bmatrix

[leaden skiff]

part of the physics package

[fathom swallow]

katie <3

[leaden skiff]

which is default in latex discord

[leaden skiff]

ayyo good job

[nocturne tusk]

swag

[toxic gale]

You mean I didn't need to do \begin{pmatrix}x \\ y \\ z \end{pmatrix} this entire time?

[surreal sapphire]

physics package

[errant merlin]

Next, can you state the limit definition of the derivative?

[leaden skiff]

do u know abt dv and pdv

also in the phys package

its based

[brittle socket]

Yeah \binom is best for the choice function

[nocturne tusk]

$\lim_{h\to 0}{\frac{f(x+h)-f(x)}{h}}$

[leaden skiff]

im still used to and prefer $^nC_r$

[fathom swallow]

Ninja

[nocturne tusk]

that looks weird

[brittle socket]

Ah yeah that works too

[surreal sapphire]

i have never seen this notation ever ninja

[nocturne tusk]

the limit

it is down

[leaden skiff]

n choose r
that was the only notation i was taught in school

[errant merlin]

I've seen $_nC_k$

[toxic gale]

That I did know. I really should use the phys package in my regular TeXing.

[fathom swallow]

feeds

katie <3

[surreal sapphire]

in general i think you need good reasons to have superscripts before a symbol

[nocturne tusk]

how do I make it not be

down

[leaden skiff]

this is fine

[surreal sapphire]

this isnt a good reason

[toxic gale]

Huh it looks right.

[surreal sapphire]

its not just fine, its correct

[nocturne tusk]

It irritates me

[leaden skiff]

oh wait yeah it was like this lmao

im dumb

[nocturne tusk]

why is the limit

down

why is it so low

[surreal sapphire]

because its a line in text

its flush at the bottom

[leaden skiff]

anyway, now try applying the limit definition to x^n

to find its derivative

[nocturne tusk]

im not doing all of that using the first principle in latex

[leaden skiff]

lol, just copy ur old latex and change it where needed

if you want write it on paper and send a picture i guess lol

[nocturne tusk]

$\lim_{h\to 0}{\frac{(x+h)^n-x^n}{h}}$

[nocturne tusk]

in car to glasgow

[leaden skiff]

no this is not correct

[leaden skiff]

lmao ok I didnt know that

[errant merlin]

let f(x) be xⁿ

[nocturne tusk]

wait no im stupid yeah

[arctic grove]

[fathom swallow]

katie <3

[leaden skiff]

yes!

now can you expand (x+h)^n with the binomial formula

[arctic grove]

ninja teacher arcs huh

[leaden skiff]

im giving back to the community

[arctic grove]

[errant merlin]

[nocturne tusk]

$\lim_{h\to 0}{x^{n-1}\binom{n}{1}+\cdots +x^0\binom{n}{n}(h^{n-1})}$

hope and pray

[errant merlin]

Well done

[arctic grove]

goooddd

now do a lil cancelling

[leaden skiff]

yes good job!

yes

[errant merlin]

Nice

[leaden skiff]

now we really wanna get rid of the h in the denominator, because if we apply the limit now we get 0/0 and thats indeterminate

so can you cancel it out?

[brittle socket]

As a side note, using the binomial formula you can prove that $\frac{d}{x^n}{dx}=nx^{n-1}$ but only for $n \in \mathbb{N}$. Iirc, if you want to prove it for all real powers you can use logarithmic (impicit) differentiation.

[fathom swallow]

grass

[nocturne tusk]

cock

[leaden skiff]

it's not \x

[fathom swallow]

katie <3

[errant merlin]

Getting close!

[leaden skiff]

yes!, now just apply the limit

[nocturne tusk]

$x^{n-1}\binom{n}{1}$

[fathom swallow]

katie <3

[errant merlin]

and what is $\binom{n}{1}$?

[fathom swallow]

feeds

[nocturne tusk]

$nx^{n-1}$

[fathom swallow]

katie <3

[nocturne tusk]

yooooo

[errant merlin]

🥳

[leaden skiff]

[leaden skiff]

here is the whole proof for reference if you wanna look thru it

[nocturne tusk]

swag ty

now I know all of maths.

all of it.

[surreal sapphire]

[leaden skiff]

knowledge is power (rule)

[errant merlin]

You are now unstoppable

[toxic gale]

[nocturne tusk]

I watched a proof of the chain rule

I understood it, but like

how would they know to do that

1 sec ill find the proof

https://youtu.be/m0LZX19DyyI

where does that second fraction come from 😭

[leaden skiff]

what fraction

[brittle socket]

The transition btw the 1st and 2nd step is just a change of denominators

instead of h at the first fraction, its moved to the second one

[nocturne tusk]

$\frac{g(x+h)-g(x)}{g(x+h)-g(x)}$

[fathom swallow]

katie <3

[leaden skiff]

this fraction is just 1 lol

[brittle socket]

That just evaluates to 1

[leaden skiff]

they multiplied by 1

[nocturne tusk]

I know

but like

why represent it

as that

[leaden skiff]

ohh like how did they come up with it?

[nocturne tusk]

yeah

[leaden skiff]

idk ¯\_(ツ)_/¯

[nocturne tusk]

lol

[toxic gale]

Normally it's just smart guesswork. In this case they want the first fraction to look like a derivative.

So getting a g(x + h) - g(x) in the denominator would make the first fraction in the form of a derivative.

But then since you can't randomly divide, you have to multiply, giving another fraction and rearranging it gives another derivative.

[nocturne tusk]

I see

yeah no I would have never come up with that

[toxic gale]

A lot of things feel like that yeah. 😂

[leaden skiff]

you've never seen it before

you get better with practice

[nocturne tusk]

actually I think I owe myself a bit of lenience cuz like

I had 2 lessons on proof by deduction and exhaustion

one of which I missed

[toxic gale]

But really the first thing you "should" think of here would be that we want to use the limit definition of the derivative with $f(b) - f(a)$, where $b = g(x + h)$ and $a = g(x)$. But that requires the denominator to be $b - a$ so we needa multiply and divide by $b - a$.

[fathom swallow]

PhenomPlasma

[nocturne tusk]

that is the only proof ive ever done

[toxic gale]

Proofs are definitely not easy when you first start.

I still find a lot of them hella hard.

[nocturne tusk]

I had one like

I forgot what it was but it involved prime numbers

[surreal sapphire]

i can confirm that i also find proofs hard

[nocturne tusk]

I had no idea where to start so I skipped it

[toxic gale]

Was it to prove there are infinitely many primes? That's usually the classic one they like to go through.

[nocturne tusk]

the mark scheme said I had to use exhaustion by representing prime numbers as (10n+1), (10n+3), (10n+7) & (10n+9)

i would have never fucking thought of that

[toxic gale]

A lot of math is like this.

There's a proof in Spivak's Calculus that pi is irrational and he just pulls these functions out of thin air.

[nocturne tusk]

oh god dont remind me

I started that book

[errant merlin]

Oof, I skipped that chapter 💀

[surreal sapphire]

hmm

[nocturne tusk]

I can hardly even do the first 5 questions on the first chapter

[surreal sapphire]

i dont think this is the original proof of irrationality

so in this case its also easier because you know the result

and then people just ask "can we prove this using wtv techniques"

and its a lot easier if you know where you want to end up

[toxic gale]

Ah yes I definitely would've come up with these functions.

[leaden skiff]

what the fuck

[nocturne tusk]

there was a question like 3^x + x < 4

that sounds easy right

[leaden skiff]

what was the question exaclty?

to find all x that this is true for?

[nocturne tusk]

find x given ghat

[toxic gale]

That can't be solved without calculator I'm pretty sure.

[nocturne tusk]

yes

[errant merlin]

find interval for x

[nocturne tusk]

Ik its like

0 < x < 1

but how do I show that

wait no

its just x<1

[leaden skiff]

its just x < 1 right

yeah

[toxic gale]

Oh wait yeah I'm dumb. You can solve it by observation.

Increasing function.

Pfft.

[leaden skiff]

yeah thats what i was thinking too, prove its strictly increasing

[nocturne tusk]

I googled it and it was using some weird ass functions

[leaden skiff]

then note f(1) = 4

[toxic gale]

Wait but if that's Spivak chapter 1 you wouldn't know calculus.

Still though I guess you would know from high school thst 3^x and x slope upwards.

[nocturne tusk]

idk if I have the exact question on my phone

[errant merlin]

I think I have it

Wait here

[leaden skiff]

spivaks calc book is really a real analysis book in disguise

afaik

[toxic gale]

Oh yeah Spivak Exercise 1.4(xii).

Up to now the only Spivak I've read is the pi chapter (I think 16).

[surreal sapphire]

you dont need calculus to show this is strictly increasing

[toxic gale]

Honestly it's an interesting proof.

[leaden skiff]

wait yeah, you just need to prove x > y implies f(x) > f(y)

[toxic gale]

Technically it doesn't ask you to prove it's correct so.

[leaden skiff]

but wait

[nocturne tusk]

the only possible solution i could think of

[leaden skiff]

no i dont get it nvm

[nocturne tusk]

was to plot both graphs and see the intersection

but idk it just dont seem right to me

[surreal sapphire]

3^(x+h) + (x+h) = 3^x *3^h + x+ h >= 3^x + x +h > 3^x + x for every h > 0 should work?

you just need some kind of argument that 3^h >= 1

[leaden skiff]

and how do u do that?

[errant merlin]

Spivak defines exponentiation much later in the book so I don't think we're expected to show that

[toxic gale]

I don't think you need to be that rigorous at the start of Spivak to be honest.

I think it's probably just there to test your intuition or something.

[surreal sapphire]

ye hm

[errant merlin]

Yup

[nocturne tusk]

oh well I havent touched spivak since that question

[errant merlin]

💀

[nocturne tusk]

idek all of precalc yet

[surreal sapphire]

maybe you do need some continuity argument

[errant merlin]

Is spivak a hard calc book or an easy analysis book

[nocturne tusk]

it is certainly a book

[errant merlin]

Definitely one of the books of all time

[nocturne tusk]

I think I still have some trig left to learn then I should be good for precalc

like radians + sec cosec and such

[brittle socket]

A calculus book that's proof based and more challenging than most

Its not really anal from what I have heard

[leaden skiff]

i dread the day i have yo learn real analysis

[errant merlin]

I guess It's a transition book

From calc to analysis

[nocturne tusk]

damn its still weird to me

that in just over a year from now ill be in uni

[toxic gale]

I'm dreading it and yet somehow slightly weirdly attracted to it.

[nocturne tusk]

finally doing more than just learning how to model the growth rate of a tree

[leaden skiff]

im someone who doesn't really enjoy pure math

so thats why im kinda dreading it lol

[toxic gale]

I mean maybe you'll learn better models for the growth rate of the tree.

[nocturne tusk]

im the opposite

applied is just really formulaic to me

[surreal sapphire]

if you study engineering you dont really have to do real analysis

[toxic gale]

I'm kinda in both camps. I like pure math a good amount but when it gets too abstract I tend to get a bit... lost.

[nocturne tusk]

tho that being said, I am only just starting year 13, so it's hardly advanced

[brittle socket]

[leaden skiff]

yeah i mean, prolly not but like i still wanna learn like physics in my free time or maybe even as a career idk, but like for that i think havinh a good grasp of real anal is necessary

[errant merlin]

I hit stackexchange after being stuck for 15 minutes

[surreal sapphire]

hmm

your average physicists probably doesnt need a real analysis class either

[leaden skiff]

ive heard many conflicting things

[brittle socket]

I only ask (here) after trying for a couple hours and running out of ideas. Imo you perhaps shld try to spend a bit more time finding a solution?

[surreal sapphire]

i feel like a lot of a real analysis class or just math classes in general maybe are focused on studying pathologies of the theory

[toxic gale]

Where I start struggling is when I have difficulty understanding the need of definitions. Like I can understand concepts like partial derivatives, eigenvalues, Jacobians, etc just fine, because I can attach it to some purpose. But when I have to define left cosets I'm just wondering OK how in the world is this gonna matter.

[surreal sapphire]

and an engineering student just doesnt care about that

[leaden skiff]

im not planning on taking like a college class on ranal btw

im gonna self study

[surreal sapphire]

and even in physics a lot of the pathologies dont appear

tho tbf i have a bad view of physics

[leaden skiff]

after i learn like algebra and la and stuff

[nocturne tusk]

self studying is too hard I can only learn stuff from classes

but I only have 4 classes a week

and im missing 3 this week 😭

[surreal sapphire]

i dont think this will work out too well if you are dreading it

you should learn NT instead

[leaden skiff]

im mostly exaggerating btw

[tiny forge]

It's because maths is kinda taught backwards. We get told definitions as if someone one day suddenly came up with it and everything just worked. When in reality they messed around with stuff for a while and eventually were like "huh this thing I'm using is pretty handy i should probably call it something and study it a bit"

[errant merlin]

Oh lol I definitely do, I was exaggerating a bit

[surreal sapphire]

tbf a good class will motivate (most) definitions

[nocturne tusk]

my adhd doesn't let me work on something for more than 5 minutes if I dont get it instantly

[leaden skiff]

like. its a lot of factors. one is that Im very bad at proofs, another is that like super abstract stuff that's also hard to understand is really hard for me to motivate myself to learn.

a lot of the ideas in ranal seem super interesting and i do wanna learn them and i do want to have a very solid understanding of math

im just worried im gonna suck at it and feel like a moron

[errant merlin]

Everybody agrees real analysis is hard

So don't worry if it doesn't click with you instantly

[surreal sapphire]

being bad is the first step of becoming good

[leaden skiff]

like ok the reason i really dread it is because i tried it once like a year ago and i almost cried because i couldnt do an epsilon delta proof

[nocturne tusk]

I dont like people putting difficulty on things

[halcyon frigate]

HELOPP

help pls

[toxic gale]

I don't think anyone can do epsilon-delta the first time they see it. 😂

[nocturne tusk]

cuz like I often struggle with shit and people just go "this is easy lol"

[toxic gale]

Difficulty is pretty much always subjective.

[surreal sapphire]

read #❓how-to-get-help

[halcyon frigate]

help bro pls

[leaden skiff]

it might literally just be that i associate ranal with those feelings now

[charred mortar]

Also chances are those ppl probably spent a lot of time on the subject before it “felt easy”

[toxic gale]

Is RA focused that much on epsilon-delta?

[nocturne tusk]

ofc, but that doesnt mean people should belittle because of that

[charred mortar]

It has quite a bit

[toxic gale]

Oh no that's not what I meant at all. I agree with you.

[charred mortar]

But there’s certainly other stuff involved too

[errant merlin]

I don't think you need it much after you use epsilon delta to proof some limit rules

Actually

[charred mortar]

It pops up here and there I’d say

[errant merlin]

Sometimes you do compute limit using epsilon delta

[toxic gale]

But at the same time I'm saying it's normal to think some stuff feels easy to you and some feels hard.

[charred mortar]

Yeah

[surreal sapphire]

epsilon delta is like

[errant merlin]

Yes

[toxic gale]

See that's what I thought.

[surreal sapphire]

you have to learn to walk before you can run

later your arguments are more intuitive

[toxic gale]

I flipped through an RA book and didn't actually see that much of it.

[surreal sapphire]

"ok so sending this guy to 0, this guy also goes to 0, so ..."

[charred mortar]

But yeah it’s often in the context of limits of some form or another

[leaden skiff]

and epsilon delta is where i learned i didnt even know how to crawl

[toxic gale]

I've tried understanding epsilon-delta so many times that it is intuitive to me now.

[charred mortar]

And there’s definitely a bunch of other stuff involved with RA yeah

[tiny forge]

Its good practice for when you go on to do analysis in more abstract spaces, where you really are going to need to use ε-δ for a lot of arguments

[surreal sapphire]

the thing is you need to be able to formally check your own work

so you have to know the definitions

later you can do "intuitive" arguments

[nocturne tusk]

idek what a limit is, I just assumed its like "as x approaches this number, the max/min value this function approaches is...."

[surreal sapphire]

but you need to learn to be self critical and be able to check your own arguments formally when needed

[charred mortar]

Later on you’ll also be able to be more flexible with the epsilons too

[toxic gale]

The actual definition is pretty much just writing out exactly what this means in terms of numbers.

[surreal sapphire]

because again, intuitive ideas dont always work

[leaden skiff]

this was the part that made me wanna bang my head against a wall
i had no idea why my proofs were right or wrong. i had no idea how to check, when i had a wrong proof i looked over it for so long and couldn't find the mistake

[surreal sapphire]

and a real analysis class will spend considerable amount of time and showing you pathologies

[nocturne tusk]

is it like

[surreal sapphire]

so you understand that

[nocturne tusk]

the closer x is to y, the more accurate it becomes

[leaden skiff]

its probably really difficult to self study ranal now that i think abt it

[surreal sapphire]

this is a thing that requires time and why i think purely self studying is not feasible for most
you need someone else to check your work and correct you, especially early on

later, you can do more things solo, but you still need sanity checks from peers

[leaden skiff]

yeah. thing is i dont want a math major, but i still want to learn these things.

[toxic gale]

That we can make f(x) as close as we want to L (this is made rigorous by saying that we can make |f(x) - L| < e for every positive e), provided x is sufficiently close to a (made rigorous by saying there exists d such that |x - a| < d). I think that's essentially the definition of limit almost done.

[charred mortar]

This I’d say is a pretty big part of the difficulty tbh

[surreal sapphire]

where i am physics majors can just take the math classes that math majors do

same for engineering

[nocturne tusk]

ah yes... words...

[charred mortar]

It can be very hard at the start to know if what you’re doing is right

[torn willow]

Epsilon delta is a useful tool for stuff

[surreal sapphire]

its more work but if they are interested

so i dunno, maybe this is possible?

[leaden skiff]

idk if this is possible for me but maybe ill look into it?

[charred mortar]

Yeah epsilon-delta helps when working in other settings too

[nocturne tusk]

only an hour till I am in Glasgow woo

[leaden skiff]

i mean maybe i could try to find a way to study with people here

[errant merlin]

Analysis study group? 😳

I'm down tbh

[charred mortar]

You could also ask for a proof check maybe

[errant merlin]

Need summer activities

[charred mortar]

In some of the channels

[surreal sapphire]

god i wish i had more free time now that its summer

[nocturne tusk]

I need other people to make me study, but everyone I know will either not know enough or be way above my level

[surreal sapphire]

i realize i am shitposting on discord for an hour already

but i am actually editing while doing so!

[torn willow]

idk if I should do ML tbh

The math seems very advanced and analysis-y

[leaden skiff]

i thought it was just la

[torn willow]

But I just don't feel like doing analysis

[leaden skiff]

and calc

[torn willow]

If you want to do ML rigorously,you need analysis

[surreal sapphire]

you need to know analysis, yes

[leaden skiff]

[surreal sapphire]

and then its a ton of numerics

[torn willow]

Just plug-and-chug feels stupid to me

ML feels very unsexy

[leaden skiff]

I assume for like just doing ML you dont need that much right.

[charred mortar]

Tbh some of the numeric stuff I’ve come across feels like putting in actual numbers instead of an epsilon

[nocturne tusk]

quick unrelated question

[torn willow]

Also MATLAB

[nocturne tusk]

what does advanced number theory consist of

[leaden skiff]

numbers

[torn willow]

Too broad

[nocturne tusk]

no way

[surreal sapphire]

it depends

[torn willow]

Probably rings

[nocturne tusk]

just like

[leaden skiff]

its like, number fields tho right

[nocturne tusk]

examples ig

[torn willow]

and integrals

[surreal sapphire]

number fields is an example, yes

[charred mortar]

All I know is that it can get ultra hard

[surreal sapphire]

thats like the original starting point of modern NT

[torn willow]

Well it uses galois theory ig

[surreal sapphire]

so uh katie

[leaden skiff]

god everything in math uses everything else

[surreal sapphire]

you know how there is the complex number i

[nocturne tusk]

yes

[surreal sapphire]

originally NT studies the integers Z

[torn willow]

So How does stats look like

Is it also tons and tons of analysis

[surreal sapphire]

an old question you may want to ask is which numbers can be written as the sum of two squares

[compact tartan]

really depends on the class

[surreal sapphire]

so x^2 + y^2

one thing you can notice that over the complex numbers this can be factored as (x+iy)(x-iy)

[nocturne tusk]

uhhhh

[compact tartan]

you could be doing the kolmogorov theorem on the convergence of the empirical distribution, or you could be like hurr durr F-test goes here

[surreal sapphire]

and this multiplicative way of writing this is much easier to study because we have a lot more tools

but there is no complex number i in the integers

so you can think of "just add it to the integers"

and this gives you numbers of the form a+bi where a and b are only allowed to be integers

now this turns out to behave somewhat like the regular integers

[compact tartan]

in stats there's some neat theory connecting estimators and tests, bayesian stuff etc, for describing "optimal" approaches

there's also a lot of measure-theoretic analysis

[surreal sapphire]

and you can define notions of what it means to be a prime number

[compact tartan]

and then there's the hard applications to actual data

[nocturne tusk]

im gonna be honest

[torn willow]

Oh damn, analysis is everywhere

[surreal sapphire]

and in fact classifying how primes behave in this thing will answer the original question

and this leads to more general questions

[nocturne tusk]

i lost you at "multiplicative"

[surreal sapphire]

oh well

the multiplicative structure of the integers is in many ways nicer than the additive

you have for example the fundamental theorem of arithmetic

so every integers can be written uniquely as a product of primes

questions about representing some number as a sum are much harder

[compact tartan]

I'd argue that's very far from "nicer than the additive"

[surreal sapphire]

its just a vibe for now

[nocturne tusk]

I think

[compact tartan]

prime factorization yields an iso between N_>1 and N^infty

[nocturne tusk]

I need to learn stuff

[compact tartan]

the latter has much more space to miss

so you get much more "no" answers

to ask interesting questions about addition you have to start with fucked up sets

hence the hardness

[surreal sapphire]

and writing x^2 + y^2 = (x-iy)(y+iy) is kind of like a factorization

oh well, i care about arithmetical questions and writing things as products is nice, writing things as sums is not

[compact tartan]

idk, weird argument

[nocturne tusk]

I need to find friends who are as dumb as me so I can talk to them without being incredibly confused

[surreal sapphire]

i tried

[nocturne tusk]

I think I probably went a bit out of my depth asking about that

[leaden skiff]

asking abt "advanced anything" will definitely sound like nonsense unless you already know a little abt it lol

[nocturne tusk]

I meant more like

more than just "a + b = b + a"

[surreal sapphire]

i dont know, those things were studied before calculus was invented

albeit with different language and generality

[nocturne tusk]

but yeah no I should defo learn the basic shit beforehand

I must learn the quotient rule...

[surreal sapphire]

i actually love the sum of two squares question because its so simple (and looks kinda dumb) but can lead to a lot of rich mathematics

[nocturne tusk]

im sure thats great and all but my brain can't comprehend it

one day maybe

[leaden skiff]

if you know the product and chain rule you can easily derive it

[nocturne tusk]

ill just do what I did with the product rule

and Google it

[arctic grove]

fuck the quotient rule, all my homies hate the quotient rule

[toxic gale]

I never remember the right order.

I always use the quotient rule to differentiate 1/x to remember which term comes first.

[leaden skiff]

low d(high) - high d(low) over the square if what's below

[neat lintel]

Left dright minus right dleft

[leaden skiff]

its a rhyme to help you remember, thats what i use

[neat lintel]

@leaden skiff 3b1b?

[leaden skiff]

yes

[neat lintel]

Same

[errant merlin]

Why remember the quotient rule when you can successively use the product, power, and chain rule everytime

[toxic gale]

I'm pretty sure it's (u/v)' = (vu' - uv')/v² but I get paranoid.

[leaden skiff]

so true

[leaden skiff]

yes

[neat lintel]

Using the product rule with the chain rule is good

For powers other than - 1

[toxic gale]

I just don't do derivatives much anymore.

When I was still in high school we rarely got straight differentiation questions because I think the teachers figured out it was too easy. Differentiation usually only appears as an application (optimization) problem.

[leaden skiff]

what are you doing now?

[toxic gale]

Slowly waiting 2⅔ years for uni to start because I have mandatory military duties coming up. So I've just been reading 1st year uni textbooks.

[leaden skiff]

[toxic gale]

Currently reading Lakins' The Tools of Mathematical Reasoning.

It's used at my uni for discrete math but its an intro to proofs book.

[bright hill]

@deep mango I remember you saying that every convergent sequence is a Cauchy sequence in a metric space

It just struck me

How tf do you make sense of convergence without a metric?

[deep mango]

What was that about wew

[deep mango]

You define it in terms of open sets

[sleek wing]

I read cauchy and convergent the other way around at first

[deep mango]

A sequence x_n converges to a point x if for every open set U containing x, there is an N so that x_n is in U whenever n > N.

This is the same thing as the usual definition of convergence in metric spaces.

[sleek wing]

yeah you use the funny neighbourhood def

[deep mango]

That definition talks about being in open balls

[sleek wing]

pftftft balls 🤣

[bright hill]

Oooo

That makes sense

[deep mango]

"x_n converges to x" means "x_n eventually stays in any neighborhood of x"

[bright hill]

Although, I'll need to learn about non-metriciazable spaces before I fully understand why we need that definition

Coz I have no idea what those look like lel

[neat lintel]

Hello! I'm trying to further increase my skill of problem solving, do you guys know any resources / books that might help me achieve this? Thank you.

[fervent pebble]

imagine doing the quotient rule

it's literally the product rule

and memorizing a whole new fkin algorithm is not worth it

[fair mural]

sorry wew but i laughed at this

[deep mango]

you apologize to wew even though your laughter is at my expense.

[bright hill]

"the art and craft of problem solving" is pretty good

it's geared towards competition math

[neat lintel]

Thank you.

[neat lintel]

"by Paul Zeitz" ?

[bright hill]

ye, probably

[neat frost]

Wow. Must suck to be you.

[deep mango]

No it's actually dope

[neat frost]

I sincerely doubt that

[fervent pebble]

idk slurp have u seen rycs hair

[neat frost]

Oh shi you’re right

[deep mango]

[bright hill]

I have no idea what I just read

[iron osprey]

x_n is stalking x

[stark charm]

so you are okay with being the butt of every joke

if i were you i wouldnt let that slide

thats just me though

[deep mango]

Humor is transactional

I am an endless hoard of patience

Better to joke about me than about someone who has a chance of being hurt by it.

[valid compass]

Haha ur profile pic is a bird ahahaha lol gottem

[dense belfry]

Lol gay bird

[cyan goblet]

how much do i have to pay

[dense belfry]

You pay in reputation

[cyan goblet]

good repsonse

[deep mango]

Lol

[dense belfry]

And you have no idea what the price is a priori

I'm pretty good at one liners tbh

[summer sandal]

I love this comment.

I have been seeing those types of comments online now for some reason.

It’s always funny; that is just me tho.

[dense belfry]

I don't think the comment was very socially aware tbh

[summer sandal]

The comment was a joke.

I believe.

[dense belfry]

I don't think it was

But maybe I'm wrong

[summer sandal]

Instigating, is what I believe it’s called.

[dense belfry]

I see

[summer sandal]

It’s a popular trend online.

[dense belfry]

What does that entail?

Trying to start a fight?

[summer sandal]

Nothing much, just jokes. Unless someone takes it too far.

By being annoying.

[dense belfry]

I mean instigating means trying to start a fight

[summer sandal]

I know.

Just I think they meant is as a joke here.

[dense belfry]

Okay

Well whatever

[summer sandal]

Lol, yeah.

[stark charm]

yea its been a thing forever

its just more popularized by ppl online now

[summer sandal]

Yeah, been seeing it online now. That why I decided to comment.

[dense belfry]

Can you please explain what it is?

[summer sandal]

Not sure why it became popular.

[stark charm]

its exactly what u said

not much else

[dense belfry]

Trying to start a fight?

That's gross

[stark charm]

lol

emma catchphrase

[dense belfry]

I have many catchphrases

They change pretty often

[stark charm]

i like it

[dense belfry]

I mean I start debates pretty often

I guess

[stark charm]

thats gross

[dense belfry]

I don't like fights though

Lol

[stark charm]

🤑

[summer sandal]

Just to let one know, I wasn’t in supports for any fights. I thought it was funny since I have been noticing those comments for a while in funny contexts.

[dense belfry]

I think the fact it's a trend is cringe tbh

Big reddit bro vibes

[summer sandal]

YouTube, but I don’t use Reddit.

Well, I do but not like discord.

[dense belfry]

Oh you think that's a more accurate description of the vibes?

Discord is nice

Honestly it's changed a lot of people's lives for the better I think

Hot take

[summer sandal]

Definitely, I used it a lot in past and people helped me a lot.

[dense belfry]

Discord is the best place for talking if you have ADHD lol

Everyone talking over each other

No need to wait

So good

[azure nymph]

Chat rooms are kinda cool in that way where you can have multiple different conversations going on and it's mostly fine

[summer sandal]

Top reason I use discord is due to its simple layout. The contents is not too much unlike Reddit and twitter.

[dense belfry]

Oh I like having multiple conversations at once in the same channel

Lol

Maximize confusion

[ancient flame]

lemme add to the confusion

[summer sandal]

That I can do, not sure how I manage to do it.

[ancient flame]

primarily bc emma is here

help what's the difference

ffs

[summer sandal]

I think there is bigger context to this.

[ancient flame]

not really

https://en.m.wikipedia.org/wiki/Maxima_and_minima

[summer sandal]

What is the definition of minimal element here?

[ancient flame]

I forget how to do it

that's precisely what im confused about

[dense belfry]

Yeah this is exactly local vs global

There being an element which is below every other element is a global minimal element

A local minimal element would be one so that there are no elements below it

I can give a concrete example

[ancient flame]

that would be appreciated

[dense belfry]

Take the partial order with three elements

a, b, c

So that a <c and b<c

[ancient flame]

what's the difference between partial order and total order

[dense belfry]

And that's it

A total order has every element is comparable

In the example I gave that's not true

a is not comparable to b

[ancient flame]

ohhhh

okay

[dense belfry]

Oh I can post a picture

For this order

One sec

[leaden torrent]

anyway, the point in emma's example is that nothing is smaller than a (so a is minimal) but a is not smaller than every other element (it's incomparable with b)

[peak tide]

standard example of a partial ordering that is not a total ordering: the collection of all subsets of a set, ordered by inclusion ($\subseteq$)

[fathom swallow]

OurBelovedBungo

[leaden torrent]

and we could interchange the roles of "a" and "b" in that sentence

and get the same fact

(i.e. a and b are both minimal)

[ancient flame]

oh ok

[dense belfry]

Yes

However c is a maximum element

[ancient flame]

that makes sense but is confusingly complicated at the same time

[dense belfry]

I have a picture

[ancient flame]

I see

[dense belfry]

If I can find a pen

[ancient flame]

okay lol

[dense belfry]

There

[leaden torrent]

though its worth noting that this example doesnt really apply to this case

the empty set is smaller than all sets

in this ordering

so it's both minimal and least

still a good example of a partial order though.

[dense belfry]

Just this

Lol

[ancient flame]

ohhhh

I see

[dense belfry]

Yeah

This is how you draw partial orders

Btw

[ancient flame]

I see

alright that all makes sense

ty guys :D

[azure nymph]

directed graph

[dense belfry]

Yes

[leaden torrent]

digraphs are partial orders

well

as long as you avoid loops

[dense belfry]

They are preorders

[leaden torrent]

correct

[errant ridge]

https://www.youtube.com/watch?v=abs-lNhneho

[slim veldt]

guys join vc

[neat lintel]

Okay so

I've seen PPL say that

You can't directly compare two complex numbers

Is taking the modulus (or magnitude) of both and then comparing them valid?

[surreal sapphire]

is i greater than 1?

[neat lintel]

Well its modulus is equal to 1

[surreal sapphire]

so?

[neat lintel]

Well we can't directly compare a complex number with a real

Complex is 2 dimensional while reals are 1 dimensional

[surreal sapphire]

what

[forest jackal]

the more informative version of this vague statement is that C does not admit an order that makes it an ordered field.

[surreal sapphire]

every real number can also be thought of as complex

[neat lintel]

They behave like two dimensional vectors* sorry

[neat lintel]

I see

[static loom]

the word "compare" here doesn't mean it in the colloquial sense if that's the confusion

[forest jackal]

you can cook up lots of "orders" if you just want to satisfy the properties an order should have (reflexivity, transitivity, antisymmetry)

For instance you could use what is called the dictionary order, and say that a+bi < c+di if either a < c (in the sense of real numbers) or a = c and b < d.

[neat lintel]

Ooh

[forest jackal]

but the point is that this order does not behave well with respect to the operations of multiplication and addition.

[neat lintel]

So there is some sort of limitation if I define an order for comparing such numbers

[forest jackal]

yes, to be precise you cannot pick an order such that the following two properties hold:

1. z < w => z + c < w + c for any complex z,w,c.
2. z > 0 and w > 0 => zw > 0.

[neat lintel]

True

[forest jackal]

you can think of these properties as saying that an order is "compatible" with addition and multiplication in your field respectively.

[neat lintel]

Thanks 👍

[forest jackal]

no worries

(By the way, it's an easy but worthwhile exercise to prove that no such order can exist. If you can't see why immediately, I suggest you think about it for a couple of minutes.)

[neat lintel]

I've been thinking about this for a while, and here's my conclusion:

1. Complex numbers are not ordered fields, i.e., total orders cannot be imposed on this field:
   Say we impose a total order ≤ on C, and assume C is an ordered field.

In any ordered field, the multiplicative identity is greater than the additive identity.

So, 0≤1
This implies i ≤ 0 ≤ 1 or 1 ≥ i ≥ 0. So i≤0 or i≥0

Taking i≤0,
In an ordered field, squares are always non-negative, i.e., 0 ≤ a² for any element a in the field. This is one of the properties of an ordered field.
Hence squaring both sides of i ≤ 0, we get -1 ≤ 0 => i² ≤ 0. This contradicts the property of ordered fields, hence contradicting our assumption.

Taking i≥0,
Implies -i ≤ 0
Implies (-i)² ≤ 0
Implies -1 ≤ 0,
which again contradicts the property of ordered fields.

2. This also contradicts the axiom a.b ≤ c.b, where b is any non negative number.
   Say 1+2i ≤ 1+3i (by comparing component by component)
   Multiplying both sides by i (positive number)
   We get -2+i ≤ -3+i
   And -2 is not less than -3, contradicting this property.

Hence, a total order cannot be imposed on Complex Field. Partial orders like ≤ where:
a+bi ≤ c+di if a≤c; or bi≤di if a=b,
can be imposed, but have limitations.

Hence, no such total order exists.

[forest jackal]

Yep, you have the main idea. Squares are non-negative in an ordered field because for any x we either have x >= 0 or -x >= 0.
In either case we have x^2=x.x=(-x).(-x) as the product of two non-negative elements and hence non-negative.

But in C we have i^2 = -1 < 0. (This last inequality following from 0 < 1 => 0 + (-1) < 1 + (-1) for example.)

[neat lintel]

Thank you for giving me such a wonderful excercise 👍

[forest jackal]

no worries, glad you were able to get something out of it!

[forest jackal]

By the way, something you might find cool if you don't know it already:

The ONLY complete totally ordered field is the real numbers.

(Completeness here is the statement that any bounded set has a least upper bound. Don't worry too much about it if you haven't seen this property before, but roughly it means it doesn't have "holes" in it like the rationals do.)

[maiden bear]

oh that's a nice one

[neat lintel]

Ohh I see
👍

[maiden bear]

a bit tricky if you don't know the "idea" to the proof maybe

[forest jackal]

Oh yeah I wasn't suggesting this second thing as an exercise, it didn't sound like the kind of thing Pencil was studying. Just mentioned it as a strong/somewhat striking result along the lines of his initial question.

[ancient flame]

Good morning, fellow individuals on the Mathematics Discord Server.

[neat frost]

Good morning moddy!

Ily!

[neat lintel]

Good morning

[ancient flame]

Hello, Slurp and Idris. How are you both doing today?

[ancient flame]

Excuse me Slurp, I do not seem to understand the meaning of "Ily." Is that a health condition?

[neat frost]

😭

My heart…..

[ancient flame]

That is a heart condition? I advise you to speak to your doctor as that is very serious.

[neat frost]

So basically for my assignment they gave us a corpus of texts and there seems to be quite a few texts about porn

[ancient flame]

That seems to be very interesting. Please enlighten me about pornography.

[neat frost]

Gmod stop acting like a fucking nerd

[ancient flame]

Excuse me, that is inappropriate behavior for this community.

[arctic grove]

[deft flame]

what kinds of functions are there other than polynomial functions?

[ancient flame]

There are exponential and trigonometric functions, for example. These can be represented by infinitely long polynomials, but they look different.

[neat lintel]

umm like

function that connect every person to his biological father

that technically is a function too

though it isn't taht useful

[brittle socket]

In general functions are just sets of tuples / ordered pairs

So you could say ${ (1,1) }$ is a function

[fathom swallow]

grass

[brittle socket]

In fact $\varnothing$ is a function

[fathom swallow]

grass

[brittle socket]

[arctic grove]

[brittle socket]

[arctic grove]

dont sully me i dont get what u are saying

[neat lintel]

$\varnothing$ maps to itself

[fathom swallow]

Llama calculus

[neat lintel]

Doing pretty good! How are you doing

[ancient flame]

im good

I gave up trying to be formal

loL

[fair mural]

good, it was weird and not funny

[open aspen]

like in text?

doing your complex impersonation?

[ancient flame]

yeah

[ancient flame]

shut up

I did it for a day a few days ago

can't do it again

lol

[open aspen]

are buisnessmen supposed to be professional and formal?

[neat lintel]

In general a function is defined as a relation, which is a subset (or equal to) the Cartesian Product of the Domain and Co-domain, and both could be any algebraic structures (Vector Spaces, Rings, Groups or even Sets). If algebraic structures are involved, we take the Cartesian Product of the underlying sets of these algebraic structures.

You can define a function as whatever as you like. Let A = {1,2,3} and B = {Coca-Cola, Chips, Amogus}
Their Cartesian Product is a set of all ordered-pairs (a,b) where a belongs to A and b belongs to B [just like on Cartesian graphs when you label points. Keep in mind (a,b) ≠ (b,a) since they're "ordered"]

A relation is what we call a function, though not all relations are functions. Relation is a set of ordered-pairs, a subset to A×B (Cartesian Product), where between a and b in an ordered pair, there exists a unique relation between them. Like a=b, a+b is even, and so on.
Here I'll define my relation R = A×B = {(a,b) | a = b}.
That's your function right there. For each a, there exists a b where (a,b) is in R and if (a,b) = (a,c), then b=c, which is true. These are the two conditions for a relation to be a function. R(a) = b, where b can be thought of as the "mapped output of a".

So R(3) = Amogus

So you can create any function you like under these conditions.
Apart from polynomial functions, you have constant function, dirac delta function, kronecker delta function, dirichlet function, absolute value function, transcendental functions (like sin(x), cos(x), log(x), e^x) and tons of others

[fair mural]

i would feel like either of them implies the other

[open aspen]

idk if formal -> professional; I can be formal and very rude, which wouldnt be professional

Not so sure about the converse

[charred mortar]

I feel like it depends on the setting

[open aspen]

in which case they are not generally equivalent

[next schooner]

Dirac delta is not a function

Also this definition of a function as a univalent total binary relation is, while correct, totally obtuse for someone who hasn't seen anything beyond polynomials

[ancient flame]

I was just doing it to fuck w y'all

[next schooner]

Much better to define a function in the usual manner, as a mapping between sets

[neat lintel]

👍

[neat lintel]

How it is incorrect?

[ionic star]

they meant correct

incorrect just sounds like correct, so you mix them up sometimes

[lunar spear]

hes using hard words like also, this and is

[next schooner]

Sorry I meant correct

Lol

[neat lintel]

Oh lol xd

[fair mural]

@next schooner i need a new rat fact

[errant ridge]

rats can hold their breath for upto 3 minutes

don't ask me how I know....

[ancient flame]

psychologist moment

[woven whale]

kinky

[void wave]

And an average cat can hold up to 2 minutes 43 seconds

[tall badge]

@brittle socket @arctic grove @neat lintel theyre not exactly functions if one requires a function's data to include a domain & codomain

[modest rune]

(as one should)

[brittle socket]

[arctic grove]

yeah, i guessed so

[velvet dagger]

Uh huh

Yeah you def guessed so

[arctic grove]

yes i did!

[arctic grove]

hence why i was confused

[velvet dagger]

@arctic grove uh huh uh huh uh huh

[arctic grove]

Dami dont bully me!

that really is why i was confused

[bright hill]

ikr

dami is a bully

+1 respect point

[velvet dagger]

ur face is a bully

[arctic grove]

[azure nymph]

What do you guys think is more efficient 6.5 hours of sleep 7.5 or 5.5

[tall badge]

its fine if the domain & codomain is clear from context, then all one has to do is describe the ordered pairs

[azure nymph]

Also does anyone have a good schedule app I wanna use my time better

[tall badge]

its just that in these cases the domain & codomain werent stated

[arctic grove]

yeah
but here there was no context 😵‍💫

[tall badge]

like to fill in the details of the 2nd example, the emptyset can be considered a function from the emptyset to any set

[arctic grove]

[brittle socket]

Yeah but btw $f: A \rightarrow \varnothing$ is not a valid function for nonempty A

[fathom swallow]

grass

[brittle socket]

just as a side note

[neat lintel]

Yes

Hmm but what about

$f: A \rightarrow {{\varnothing}}$

[fathom swallow]

Pencil/Idris

[neat lintel]

[peak tide]

certainly allowable, as is $f : A \to {\emptyset}$

[fathom swallow]

OurBelovedBungo

[neat lintel]

👍

Yeah I forgot ∅ is itself a set lol

[peak tide]

yep

[rose dock]

7.5

although for me it's probably close to 8.5

[arctic grove]

anything around 8 hour is good

[neat frost]

What does “efficient” mean in this case?

Pretty sure teenagers are supposed to get between 8 and 10 hours of sleep

So if you meant “healthy” then none of those

[arctic grove]

yeah, but if not possible, at least 8 is fine

[neat frost]

No

It’s 8 and 10 not inclusive

Gotta make sure you at least get 8 hours, 1 minute

[arctic grove]

ofc

lol

but yeah u need at least that much sleep

and at no point in ur life do u not need that much sleep

[deep mango]

I got 5

That's more than enough

Stop wasting your time asleep lazies

[neat lintel]

5-6 hours is more than enough actually when you are in highschool

[deep mango]

[neat lintel]

Wat

[deep mango]

I hope you are trolling the troll

[neat lintel]

[charred mortar]

Sleep deprivation is not good

[rose dock]

unfortunately it's normal for a lot of high schoolers

[charred mortar]

Yeah alas it is

In highschool my priority was usually to sleep really

But I know many of my classmates were sleep deprived (and understandably so)

For me I’d be willing to potentially do some hw or whatever badly if it meant I could get my proper sleep in

[ripe wasp]

when should i be sleeping during the summer?

i sleep around 11:30-12 then wake up at around 9

[charred mortar]

I tend to just sleep at a reasonably regular time, say 11 pm to 8

That seems fine to me

[neat lintel]

I sleep at 12 am at wake up at 6:30 or sometimes at 6 am

[ripe wasp]

one of my friends sleep at literally 8 pm then wake up at 4...

[rose dock]

time for the grindset

[ripe wasp]

he's like the model ideal student bro studies and does all of his homework the day its assigned and shit

im happy for him, his work paid off

he got into a very prestigious boarding school

[bright hill]

people need less sleep the older they get

sooooo, checks out, grampa

[deep mango]

Well

Judging by my state right now

I need to sleep more

[neat frost]

5?!! You have that much time?

[deep mango]

Yes

[neat frost]

Wow

Guess you have less stuff to do as you get older

[bright hill]

"Browsing Reddit and chatting on discord till 5 am" don't count as "stuff to do"

[neat frost]

Wow Reddit? What are you, a loser?

[bright hill]

I'm referring to you lel

[neat frost]

I understand

I was referring to how you immediately jumped to Reddit

You were obviously projecting

[bright hill]

I don't sleep at 5 am.

[deep mango]

I browse reddit

But I don't sleep at 5am

[bright hill]

Ye, I found your account the other day lel

[deep mango]

I sleep at midnight and just wake up at like 6

😮‍💨

yes I made an account so that people could see it if they wanted

since all i do is post on the big brother and survivor subreddits

and give ridiculous takes about reality television

[bright hill]

Lel

Based

[bronze pelican]

Ryc stands for reddit yuser cringe

[bright hill]

[errant ridge]

[arctic grove]

not at all

smh

[bright hill]

It's true tho

You can look it up

[arctic grove]

its not true

u always need 8 hours of sleep, no matter how old you are

[surreal sapphire]

infants needs a lot more

and sleep times go down with age in general

this is the better image

[bright hill]

Get rkt

[arctic grove]

its still around 8

fairly close to it

it didnt get to 5 hours

[surreal sapphire]

ye

there are some people that can do with 5 hours

there is some genetic predisposition

but its not the norm

[arctic grove]

.

[arctic grove]

thats rather rare

[surreal sapphire]

i mean this is still true

[arctic grove]

those people can get rem sleep quickly

[surreal sapphire]

sleep required goes down

[arctic grove]

but not to 5 hours

[surreal sapphire]

there is also thing thing that if you sleep more often, you need less sleep

[arctic grove]

true

[surreal sapphire]

the general ideas is that the deciding factor is REM sleep, not time spent asleep

and if you sleep more often, you get more REM sleep

[bright hill]

Ye, but that's not what I said lel

[arctic grove]

[arctic grove]

yeah, ik

[bright hill]

Ok, maybe when I was messing with ryc

[arctic grove]

thats what i was talking about!

[bright hill]

Does anyone know how edd is doing?

I miss edd

[ancient flame]

wait where is he

[bright hill]

I dunno

Ryc said they were on a break way back

[ancient flame]

oh ok

[ancient flame]

my grandma be like

she sleeps like 10 pm - 3 am

literally

meanwhile I sleep 3 am - 10 am

and I am still tired af

my body needs like 9 hours of sleep

I was sleeping well at the start of summer but my dad kept getting mad I slept until 11 am

actually now I wake up at like 9 am

I keep trying to sleep earlier but I can't