serious-discussion

[dapper badge]

iirc one thing is that matrix algebras over C just get mapped to the empty space which feels wrong

[full isle]

huh?

matrix rings you mean?

ig calling them algebras works too

[dapper badge]

basically same thing

[full isle]

but idk what prime ideals even look like lol

[dapper badge]

yeah prime ideals for noncommutative rings get a little weird, I think the most popular definition is via the prime condition for ideals meaning that if AB is in P, then A is in P or B is in P, where A and B are ideals

[full isle]

no shit lol

what else do you mean?

thats the definition lol

[dapper badge]

well for commutative rings its on the level of elements

which I suppose one could replace by principal ideals

which I would argue is where the generalization comes from

[full isle]

bruh what r u meaning

its the same thing

the definitions are equivalent am i crazy

[dapper badge]

the definition on the level of elements doesn't work for noncommutative rings, does it?

[full isle]

maybe?

i just assume its left and right prime ideals

but ig maybe that isnt helpful

[dapper badge]

idk, tbh haven't thought about prime ideals in noncommutative rings too much

[full isle]

same here

hard to think about

also idk a lot of examples

[pure sun]

are you specifically talking about "spec" of a noncommutative ring?

[dapper badge]

yeah that's what I was referring to in my reply to mizalign

[pure sun]

i see

yeah spec just doesnt really make sense in a noncommutative setting

even without going into more technical reasons why the naive definition doesnt work, it morally shoudlnt work

(my advisor told me this one and i thought it was really cool)

rings should be thought of as rings of operators

(think of like C[T] acting on a vector space for motivation)

[dapper badge]

makes sense, I like endomorphism rings

[pure sun]

the spectrum of a linear map is related to the spectrum of the ring C[T]/p(x) where p(x) is the char poly of the operator

one thing you learn in linear algebra is that commuting operators can be simultaneously diagonalized

and so it makes sense to talk about the simultaneous spectrum of commuting operators

[dapper badge]

😮

that's a really neat way to think about it

[pure sun]

but with noncommuting operators, you just can't

and so morally spec of a noncommutative ring just shouldn't exist

[dapper badge]

I like that a lot, will definitely keep in mind

also, just because I don't know lol

[dapper badge]

what's the actual relation here?

[pure sun]

Spec(C[T]) is just C

the maximal ideals being (T-a)

a vector space V with a linear operator A is the same thing as a C[T]-module

[full isle]

i didnt know this

[pure sun]

The C-module comes from it being a vector space and T acts via A

[full isle]

so what is vector space R as a C-module?

[pure sun]

as a C[T]-module, this pair (V,A) is isomorphic to the C[T]-module C[T]/p(T) where p is the char poly of A

[pure sun]

it's not one

C-modules are vector spaces over C

[full isle]

yes

[pure sun]

and C[T]-modules are vector spaces over C with a linear operator

[full isle]

so why did you say let V be a vector space

[dapper badge]

is Spec C[T]/p(T) the linear factors of p?

[pure sun]

there is a natural map Spec C[T]/p(x) into Spec C[T] which is just C

and the image is exactly the roots of p(x)

i.e. the eigenvalues of A

[dapper badge]

ahhh yeah I probably should've figured that out on my own

but still really cool!

[full isle]

So A is supposed to be a linear operator

[pure sun]

because i assume my readers can understand from context

that of course i'm talking about vector spaces over C

given that i had said C was my base field several tiems

[full isle]

so do we choose linear operator A?

[pure sun]

A can be any linear operator on V

the data of a C[T]-module

is exactly the same as the data of a COMPLEX vector space V and a linear operator A on V

[full isle]

ig seeing an example would be kinda cool

ill try and do one

[pure sun]

i mean

[dapper badge]

just bc I'm complete beginner at alg geo and wanna make sure I have full understanding, Spec C[t]/p(t) is the set of principal ideals generated by the linear factors of p

[pure sun]

what is your favorite n x n matrix?

that can be your A acting on C^n

[full isle]

yeah

[dapper badge]

and each of these ideals corresponds to the point which is the root of said linear factor

[pure sun]

in a literal sense it's the prime ideals of the ring C[t]/p(t)

[dapper badge]

which are precisely the eigenvalues!

[pure sun]

it's a general fact that the prime ideals of R/I are exactly the prime ideals of R which contain I

C[t] is a pretty simple ring, and the prime ideals are all of the form (t-a) (excluding hte 0 ideal which im ignoring for now)

and p(t) is in the ideal (t-a) if and only if p(a) = 0

eigenvalues of A <--> roots of p(t) <--> prime ideals of C[t] containing p(t) <--> prime ideals of C[t]/p(t) = Spec C[t]/p(t)

[dapper badge]

perfect, that's essentially the line of reasoning I had in mind

[pure sun]

nice!

[full isle]

oh thats really cool

[ancient flame]

𝔤𝔪𝔬𝔡

[fierce abyss]

@empty mantle It wasn’t very detailed. What I meant was that you use CRT and primes =1 or 3 mod 4. Notices that 3^4=1=1^4 mod 16

[empty mantle]

Thanks

[stable ginkgo]

Can someone say the step by step evaluation of mul because the 0 numeral confuse me

ADD(n,0) returns n to which (ADD(n)) is applied

That makes sense but will the 0 numeral get composed everytime we apply the function too?

The syntax confuses me

[compact tartan]

there's no ADD(n, 0), only ADD n 0

you're applying one argument at a time

remember that m f z (where m is a number) means to apply the function f m times to z

so m (ADD n) 0 means to apply ADD n m times to 0

so it's gonna be $\underbrace{<ADD> n (<ADD> n \dots (}_{\text{$m$ times}}0) \dots )$

[fathom swallow]

mniip

[compact tartan]

there's a better definition for MUL btw

$$<ADD> = \lam n \lam k \lam f \lam z n f (k f z)$$
$$<MUL> = \lam m \lam n \lam f m (n f)$$
$$<EXP> = \lam m \lam n n m$$

[fathom swallow]

mniip

[tender tulip]

i don’t see the problem with prime ideals of noncomm. rings

[stable ginkgo]

that clears it up thanks im really dumb

[stable ginkgo]

lol much nicer thank you

[ocean thorn]

so yea as i was saying

[bright hill]

bruh moment

[neat lintel]

30-50 = -20

[neat frost]

Do people seriously have inner monologues?

Weirdos

[bright hill]

you don't?

[neat frost]

No?

[bright hill]

wha

like

wtf is thinking to you?

[neat frost]

My brain is hella weak no cap

[neat frost]

No clue I’ve tried… thinking… about that and I just don’t know

[bright hill]

[neat frost]

Anyway DarQ my brain can’t do shit

[bright hill]

can't you talk in your head at all?

[bright hill]

hm?

[neat frost]

No I can talk out loud tho

[bright hill]

are you trolling me rn?

[deep mango]

not having an internal dialogue

[neat frost]

Not at all

[deep mango]

[bright hill]

like

[deep mango]

Please don't advertise paid tutoring services on this server

[neat frost]

I’m curious if there’s an issue with my brain

Because I can’t visualize

[deep mango]

It's not an issue

[bright hill]

so you have never stayed awake coz you brain can't shut the hell up?

[neat frost]

And I can’t converse internally

[deep mango]

darq is doing a good job of making our thing sound like the issue

[neat frost]

Like I have worries or whatever but they don’t manifest as voices, they’re just… thoughts

[deep mango]

how do you sense the thoughts

[neat frost]

I don’t know?

They’re just there

[deep mango]

it's not like i ACTUALLY hear a voice

but vaguely, they manifest themselves as heard

[neat frost]

I talk to myself a good bit

Like when I’m thinking

[deep mango]

I can't see them written down like a script in my head

[bright hill]

this is so weird

[neat frost]

Tbh I’m not sure

[bright hill]

I think I don't actually have an inner dialogues, it's just that it's the way my brain makes sense of my thoughts

[deep mango]

It's sort of hard to put your finger on it

[bright hill]

or smth

[neat frost]

Because now that I think about maybe I do have an inner monologue

[deep mango]

well

[neat frost]

But like

[deep mango]

this is why i get freaked out

cause people always call it an inner monologue

[neat frost]

I may confuse it with talking to myself?

Idk

[deep mango]

but monologues don't argue with themselves

[neat frost]

I don’t have a good memory anyway so I can’t remember what I’m like

And then if I think about having an inner monologue I can think conversations to myself so that doesn’t work

[deep mango]

but then i'm like "hey is it weird that sometimes it's two brain voices talking to each other" and they're like "no, that's fine"

[neat frost]

If that makes sense

[deep mango]

so why the fuck are you calling it an internal monologue?

[neat frost]

So basically I’m a man of mystery

[neat frost]

Me?

[deep mango]

no the person who i am talking to

[neat frost]

Oh

Oop

[deep mango]

that person is my therapist

[bright hill]

[deep mango]

lol

[neat frost]

Yeah no I cannot relate to this

[bright hill]

I used to have characters inside my head

who talk to each other

[deep mango]

oh yeah

[neat frost]

A lot of my thoughts manifest as urges tbh

[deep mango]

when i was a kid i came up with like

[neat frost]

Oh okay so I’m not like you guys at all

Good good

[deep mango]

big complicated worlds and casts of characters which interacted

it's weird how i can only do small scale stuff now

[neat frost]

Damn that’s actually cool

[deep mango]

no it wasn't cool it was very cringe

[neat frost]

Imagination to age is an inverse relation

[bright hill]

I still have characters in my brain

two

I call them ego and monkey

[deep mango]

and is probably partially why my interests are fucked up now

[neat frost]

Evil DarQ and annoying DarQ?

[bright hill]

[neat frost]

Oh

[deep mango]

this checks out

ego is evil darq and monkey is annoying darq

[neat frost]

You guys are so funky

Lowkey multiple personalities

[deep mango]

yeah i was worried about that but apparently this is also like

an anxiety symptom or something

[neat frost]

Oh

[deep mango]

and isn't that serious

as long as it's not like

[neat frost]

Really?

I’ve never had anything like that

[deep mango]

LITERALLY hearing a voice in your ear telling you to kill people like fucking Jason

well it doesn't have to be there for everyone

it's not a universal symptom

[bright hill]

:)

[neat frost]

Yeah

[deep mango]

i'll be honest with you slurp

[neat frost]

But that’s so interesting

[deep mango]

i'm still skeptical

[neat frost]

Never heard of this

[deep mango]

i think there's a good chance that one day i'll just snap like a twig

and then what will I do first!

[neat frost]

Wow

So funny

[bright hill]

[neat frost]

I bet your voices all love me

[bright hill]

the first I'm gonna do when I inevitably become a mod is ban slurp

[deep mango]

my voices don't have likes and dislikes weirdo

[bright hill]

slurp, this is a promise

[neat frost]

The first thing I do when I become mod is advocate DarQ for honorable

[deep mango]

huh

i wonder if you two can figure out

[bright hill]

bitch, I'm already honorable

[deep mango]

who's closer to honorable / mod between the two of you?

[neat frost]

No DarQ feel guilted

[neat frost]

DarQ probably

[deep mango]

there we go

[neat frost]

Like unironically

[bright hill]

lol

[neat frost]

Jk it’s an arbitrary system

[bright hill]

I mean

[neat frost]

That implies there is a ranking

[bright hill]

I help out a little sometimes

[neat frost]

Instead of mniip deciding on a whim

I do too DarQ

[deep mango]

it's not just mniip deciding on a whim! sometimes it's daminark or namington instead!

[neat frost]

Also I’m ryc’s favorite member

[bright hill]

you literally do nothing but bitch in discussion and abuse latex in #latex-testing

[deep mango]

[deep mango]

second favorite at most

[neat frost]

Mniip and his alts

[deep mango]

come on

[neat frost]

At most means less than or equal 2, ie 1 or 2

[deep mango]

that's

not how that works

[neat frost]

Yes it is

I’m gonna tell shin

[deep mango]

tell him what

[bright hill]

everyone knows who's ryc's favourite

get a grip, slurp

[deep mango]

what!?

[neat frost]

I’m telling shin that he has a 50% chance of being ryc’s favorite

[bright hill]

that'd be me ofc

[neat frost]

Yeah no

[deep mango]

i don't have a favorite user. that would be strange

[neat frost]

Yes you do

Me

[deep mango]

that's like having a favorite child

[bright hill]

ryc is the server's father

[brittle socket]

Hi Chalk!

[deep mango]

hang on people are slandering pdes

[lethal flame]

hello there

[deep mango]

Welcome

[deep mango]

Hello grass

That is great

[neat frost]

All parents do have favorites

[deep mango]

It's just equal to 0

although this is interesting

[neat frost]

I know because I’m definitely not either of mine

[deep mango]

because there are programming languages which actually have a separate -0 for silly reasons

how is it different?

i just get 0 both times

uhhh

[neat frost]

Lol shitty calculator

What calculator is this

[deep mango]

something is being entered wrong there somehow

[deep mango]

you're not my favorite of your siblings either

[neat frost]

But like how could you fuck with the order of operations to even get 5

[neat frost]

Which one is?

[deep mango]

your older brother

[neat frost]

Yeah but ryc has a phd

No -0 is 0

[deep mango]

i don't have a phd

[neat frost]

Yes you do

You have an honorary one from slurp university

Honorary because you’d fail all the courses in a real uni

[deep mango]

[neat frost]

You don’t even know him

Though he is cooler ngl

[deep mango]

I know enough!

[neat frost]

He has like the same personality as you

But a computers dude instead of a math dude

[deep mango]

maybe this is some dumb floating point thing

[deep mango]

oh, no way then

ew

[neat frost]

Nah I’m kidding he’s not like you

You don’t know how calculators store their inputs

[deep mango]

i don't understand what your angle is here

[ancient flame]

theta

I can count to 31 on one hand

[deep mango]

loaded up

[ancient flame]

smh

[bright hill]

I'm not my parents' favourite, I know that

[neat frost]

Oh ryc

I think

[deep mango]

i don't think i'm my parents favorite but that's because they're too nice to like their most successful kid the most

[ancient flame]

im my parent's most favorite

...and least favorite

[neat frost]

You’re the oldest

[deep mango]

yes

[neat frost]

So

[deep mango]

yeah but like

come on

[neat frost]

Ofc you’re the most successful rn

And also

No one likes the oldest

[deep mango]

we can all see the trajectories here

[bright hill]

I think I'm not my parents' favourite coz they know I hate em

[arctic grove]

[deep mango]

If I am the discord dad

[neat frost]

I’m not my parents favorite because I’m the middle child and the system is built against me

[deep mango]

then shyshu is my favorite discord child

[arctic grove]

but u are a toddler, so ur parents love u

[arctic grove]

[neat frost]

Fook off

I’m your favorite discord nephew at least

[neat frost]

No

[deep mango]

ur like the weird uncle who shows up to family reunions uninvited

[neat frost]

Yes

[deep mango]

you can be my favorite one of those?

[neat frost]

I’ll take it!

[bright hill]

[arctic grove]

if u are the only one of a kind

u are the best

[neat frost]

Otherwise known as the “cool uncle”

[bright hill]

what am I then?

[arctic grove]

u are darq

[neat frost]

The annoying toddler everyone secretly wants to smother

[deep mango]

nephew's friend's gf's brother

hahahaha

[bright hill]

does that mean I have a sister?

[arctic grove]

thats one implication

[bright hill]

lol

[deep mango]

what a strange takeaway

[bright hill]

hahaha

[deep mango]

yeah

[neat frost]

Hey DarQ I’m curious, what language is your inner monologue in?

[bright hill]

english

[neat frost]

English isn’t your native language tho right?

[bright hill]

I think I also dream in english now

ye

[neat frost]

So was it like a gradual change?

From inner monologue in other lang to English?

And dreams?

[bright hill]

I just hated my native language

and refused to use it in my only safe place (back then), my mind

[neat frost]

Inchresting

You’re an interesting character DarQ

[bright hill]

uh

thanks

lol

[neat frost]

Not a compliment

You’re a weirdo

Jk lub ya DarQ

[bright hill]

lol

STOOP

YOU'RE MAKING ME SMILEE

[hushed turret]

strange discord family

[bright hill]

fuck you @neat frost for making me smile

[neat frost]

DarQ rn 🤡

[neat frost]

Yeah those mouth muscles are gonna be the only muscles getting any use today I’d bet

That and your right hand

[bright hill]

I type with two hands

I'm not a caveman

[bright hill]

also, yes

[cyan goblet]

missed the joke

[bright hill]

today is my rest day

[neat frost]

Yes… type… that’s what I meant yes…

Hey anemone

[cyan goblet]

yo

[neat frost]

Wassup dawg

[cyan goblet]

nm u?

[neat frost]

Same same broski

[cyan goblet]

“Wassup dawg”

[neat frost]

Nice DarQ

Nice

I respect that hustle

[bright hill]

[neat frost]

You’re such a shyshu wannabe

[bright hill]

what does that mean?

[bright hill]

what does THAT mean

[neat frost]

Oh I’m so smol and innocent and WEIRD and a WEEEEEEBBB

[cyan goblet]

ugh time to go shopping for dorm stuff

lata chat

[bright hill]

bye anemono

[neat frost]

Chow chow my little fluffernutter

[cyan goblet]

tf

[bright hill]

@arctic grove slurp is calling you a weeb

[neat frost]

And away you go my little poofersack

[neat frost]

Yes yes

Okay see ya later you fucking square

[deep mango]

[neat frost]

(To DarQ, not you anemone)

[neat frost]

TYPING ryc, TYPING

[deep mango]

Oh apparently my hand configuration while typing is weird

get this

[bright hill]

[arctic grove]

What the fuck

[deep mango]

my left hand is vertical, my right hand sits at a 45 degree angle

[arctic grove]

I am no weeb jfc

[deep mango]

my left hand goes shift, s, e, f, space

my right hand goes mousepad, n, j, k, ;

and then the right hand pivots on the wrist

and the left hand shifts back and forth laterally

the thing is, i was telling alex this

and he was like "lol you're so weird" as he usually is

but it turns out his hands look like a fucking spider on the home row!

[arctic grove]

Alex?

[cyan goblet]

ryc i think you would like a split keyboard

[deep mango]

my fingers are all naturally extended

[deep mango]

justalex

[ancient flame]

always remember to langle your rangles

[deep mango]

ew i'm not some keyboard nerd

[arctic grove]

Oo u know them irl?

[cyan goblet]

my bad

[deep mango]

no

[ancient flame]

[arctic grove]

Thonk

[bright hill]

why the sully?

lol

[ancient flame]

idk

[arctic grove]

Oh u were telling

[ancient flame]

lol

[arctic grove]

Reading on mobile is harder

[deep mango]

imagine knowing that guy irl

that would be a pain

[arctic grove]

Just know me irl

[ancient flame]

imagine knowing me irl

[deep mango]

imagine knowing that guy irl

[ancient flame]

poor metal (shortly)

[deep mango]

that would be a pain

[arctic grove]

That?

[ancient flame]

9 days!!!

[bright hill]

hm?

what does that mean?

[ancient flame]

hehe

[deep mango]

i read some math this morning

[arctic grove]

Gmod will go to the same uni as metal

[deep mango]

finally

i'm going to keep reading soon, it has grabbed my attention

[bright hill]

wait what

how old is metal?

[deep mango]

https://arxiv.org/abs/1901.09023 this paper

[arctic grove]

Ish

[bright hill]

WTF

[ancient flame]

lol

[arctic grove]

He Is 3rd year student

[deep mango]

[arctic grove]

Oh I shouldnt

[deep mango]

what is darq on today

[arctic grove]

Dox metal

Lol

[deep mango]

yeah you should tell them all my home address while you're at it

[arctic grove]

Ok

Rycs address is flat number 420

[deep mango]

no no no wtf!

[arctic grove]

69th Avenue

[deep mango]

please don't order pizzas to there

[arctic grove]

Oh ok

I stop

[deep mango]

as long as they never figure out the city, i'm good

[arctic grove]

Ryc is from nyc

[deep mango]

wtf...

[bright hill]

lmao

[ancient flame]

bryclynn

[bright hill]

do you expect me to know every person on this server personally?

[ancient flame]

yes

[tight comet]

yes

[bright hill]

I wish, tbh

[deep mango]

strange wish

[bright hill]

there are a lot of really cool people here on the server which I'd like to get to know

[errant ridge]

yes, you should know me personally

[bright hill]

I'm talking about the core community

not all the 90k member lmao

[tight comet]

Aw, am I part of the peripheral community

This is discrimination

[full isle]

Hi

I have a fun problem I think?

[ancient flame]

youre not even there

[errant ridge]

am I there

[tight comet]

But it's either core or not-core

[bright hill]

yes

[errant ridge]

imagine having the ability to know 90k people personally, what would it look like?

[bright hill]

[tight comet]

https://en.wikipedia.org/wiki/Dunbar's_number

[compact tartan]

no we consult beef.xls

[errant ridge]

yea I've heard of that

[tight comet]

not xlsx?

[errant ridge]

.exe

[bright hill]

even if you were able to get to know a person in a day

that'd take you...

[errant ridge]

246 years?

I'd just extend my lifespan

currently I know no one outside my immediate family personally

[bright hill]

I have a lot of questions concerning this message

[compact tartan]

it's actually a google sheet

[tight comet]

Why are you using microsoft extensions on google sheets

so many questions

[bright hill]

google sheets don't have an extension

you can export to several formats tho

[compact tartan]

you can import from csv and that's what matters

[tight comet]

csv is a very 'raw' data format, so it better be accepted

[compact tartan]

@quasi jetty generates a bunch of things in CSV

[errant ridge]

what's the difference between csv and xlsx?

[bright hill]

apparently a lot of small businesses use google sheets as their database of choice

[compact tartan]

csv is merely a sequence of rows each containing simple strings

[bright hill]

kinda creative, ngl

[compact tartan]

xlsx is a complex format describing a smart spreadsheet with tons of formatting and a formula language

[neat frost]

Oh ofc ofc

Why beef

[bright hill]

TF IS beef.xls???

[compact tartan]

it contains a matrix of who has beef with whom

[neat frost]

Ah

[bright hill]

oh

[neat frost]

How much beef do I have

[errant ridge]

I see

[neat frost]

At least 3

[arctic grove]

and how much do i have

[neat frost]

If I had to guess

[compact tartan]

sorry that is classified information

[arctic grove]

must be 0

[neat frost]

Is it more than 3?

[arctic grove]

come on, im just asking about myself...

[errant ridge]

none because you're indian

[bright hill]

how much beef is there?

[neat frost]

At least 3 DarQ

[errant ridge]

true

[compact tartan]

the story actually is that we've been slacking on nominating people for roles for a little bit

so we kinda compiled a huge list yesterday

[errant ridge]

am I in that list

I bet I am

[arctic grove]

Nominate me for trusted!

[bright hill]

oh

[arctic grove]

or honorable, i wont mind either

[neat lintel]

rusted*
(jk)

[errant ridge]

yea we should create a new role for shyshu "rusted"

[bright hill]

nominate me for mod

I need the lighter shad of blue

[arctic grove]

I need it more than u

[bright hill]

actually, you can take out the mod perms for all I care

[arctic grove]

cyan suits me better

for me too!

[neat frost]

Hey Shawshank!

[bright hill]

all i need is the lighter shade of blue

[arctic grove]

i dont care about the perms

i need that color

[neat lintel]

hey Slurp

wanna go see the iron dome ?

[neat frost]

Sure?

[neat lintel]

ok

[neat frost]

Are you near a battery?

[errant ridge]

mfw when people are wanting different roles not because of more access but because of the different colored name

[bright hill]

inb4 mniip actually gives me cotton candy color when in reality I hate it

[neat lintel]

not exactly

but

[neat frost]

[bright hill]

I should've picked up a different color for the joke

[arctic grove]

color matters

[neat lintel]

my mates dont understand this discord emote shit that i've managed to pick up

[arctic grove]

like a lighter shade of blue!

smh

[neat frost]

Lol

[errant ridge]

shyshu dont be racist

[neat lintel]

they feel i'm de-boomering

[errant ridge]

[arctic grove]

wtf

[neat lintel]

and idk if its a good thing or not

[neat frost]

It is a good thing

[errant ridge]

Lmao im kidding

[neat frost]

Don’t worry

I’m not

@arctic grove your racism will be tolerated no more

[compact tartan]

being on the list is not necessarily a good thing

[errant ridge]

[bright hill]

I want this color

[arctic grove]

im not racist!!!

[errant ridge]

is that a threat....

[neat frost]

That’s what a racist would say!!!

[arctic grove]

but am i there

[arctic grove]

oh shut up

[errant ridge]

that's what a racist would say

[bright hill]

it's ever so slightly different from the very active role but it's SOO much better

[neat frost]

Shyshu has been exposed

[errant ridge]

exposed!

[arctic grove]

yesss

[arctic grove]

wtf

[bright hill]

@compact tartan can we please change the very active color to this?

[neat frost]

No the very active color is meant to be ugly

[arctic grove]

and can i please get very active

[hushed turret]

now im curious

[neat frost]

Being very active is not a reward

It’s a sign of shame

[arctic grove]

its not ugly

[neat frost]

Ryc will back me up on this

[deep mango]

with what

very active is the best color

[neat frost]

Very active is a sign of shame

And not a reward

[deep mango]

active is unreadable on dark mode

[errant ridge]

nah mod is the best colir

[neat frost]

@neat lintel what happened with the iron dome?

[tight comet]

the reward was all the friends we made along the way uwu

[errant ridge]

[bright hill]

actually true

BUT IT COULD BE SO MUCH BETTER

[neat frost]

I like mniips color

Pink ftw

[bright hill]

i dunno

[neat lintel]

nothing except that it's being effective 💪

[bright hill]

pink is sortta

[neat frost]

But

[bright hill]

too pink

it weirds me out

[neat frost]

How do I see it?

[neat lintel]

oh you can't afaik

i was

kidding

[neat frost]

What

Evil evil man

[neat lintel]

[neat frost]

Anyway shaw are you familiar with b trees

[errant ridge]

green is the best color in all of existence, 530 nm wavelength ftw!!

[neat frost]

Dude shut your nerdy-ass mouth

[neat lintel]

not with operations on b trees, rn i just know how to make one

[errant ridge]

make me

[neat frost]

I fuckin hate those shits

[bright hill]

blue is just superior in every facet

[tight comet]

how do you know it is 530?

[neat frost]

I made a mistake with them on my test yesterday

[bright hill]

(almost) black is better ofc

but blue isn't that bad

[errant ridge]

because I invented it

[neat frost]

Like there were 2 values in a node, and I only drew two children

[neat lintel]

oof..

[neat frost]

Yeah and like

That’s a small mistake

The essence of my answer is still there

[neat lintel]

[neat frost]

But the question itself wasn’t so complex so like it’s sorta a big deal?

It was prove/disprove that if you enter a value in this kind of state then the height must change or whatever

And I gave a counter example but my tree was wrong, but the idea’s there

[deep mango]

ughhh

[neat frost]

But the question is worth 12 points

[deep mango]

i'm losing nitro in 6 days

[neat frost]

Oh?

[neat lintel]

hmm, then its a lost battle...

[deep mango]

my cute doggy banner will go away

[arctic grove]

[neat lintel]

maybe try to negotiate it with the teacher

[neat frost]

I wanted to get a good grade tho… ;-;

[arctic grove]

im losing in a month

[tight comet]

nice bond banner

[neat frost]

No they’re terrible with that

They like docked points off of everyone who requested a review

[bright hill]

shyshu, how come you're not very active yet?

[arctic grove]

i have no fucking clue

[neat lintel]

wtf that's horrible

[arctic grove]

the bot just hates me

[neat frost]

Yeah

They always say it’s a possibility

But still kind of an asshole move to actually do it

[devout nacelle]

Wtf I love AI uprising now

[deep mango]

the bot has been trying to make you very active but we keep vetoing it

[errant ridge]

Lmaoo

[neat frost]

The BUTT

Don’t touch the BUTT Nemo!!!!!

[arctic grove]

wha---

im sorry what!

[neat frost]

Hi sorry I’m slurp

[arctic grove]

why would u do that??

[errant ridge]

yes shyshu that's true, that's why i got active before you got very active

[arctic grove]

[neat frost]

DarQ failing twice in a row to select peach is funny

[arctic grove]

what the hail...

@deep mango remove the veto

right now.

[bright hill]

thrice actually

[full isle]

I think I realized something

Mappings between posets can be seen as braids

made into*

[errant ridge]

posets are weird change my mind

"partial order"

eugh

[wooden flax]

No they're not

Lmao

[errant ridge]

[wooden flax]

They're fairly natural

[errant ridge]

really?

what even is a partial order? things are ordered or not ordered, THE MATHEMATICIANS HAVE BEEN LYING TO US, WAKE UP SHEEPLE!!

[neat lintel]

i agree, preordered sets are much more natural

[wooden flax]

@deep mango when will I get active

[errant ridge]

so anyway what is a partial order?

[neat lintel]

often you have situations where 2 things are not comparable

[errant ridge]

i don't entirely get it

[errant ridge]

like they have the same "magnitude"?

[neat lintel]

for example lets say there are 2 computers: one has better cpu speed other has better gpu speed

then you cant compare those two

but if you have another computer with cpu and gpu higher than both

[errant ridge]

ahh

right

[neat lintel]

then that one is better than the other ones

[errant ridge]

so mathematically how is it defined?

a PO on a set

[neat lintel]

its a set along with a binary relation <= such that x<=x (something is as good or better as itself) and if x<=y and y<=z then x<=z (if y better than x and z better than y then z better than x

and in partial orders you also have if x<=y and y<=x then x=y, which is kinda weird to justify, if you use preorders then that is not required

[errant ridge]

right, so it has to be transitive

[errant ridge]

it kinda makes sense I guess?

[neat lintel]

transitive and reflexive

and symmetric if you want partial order and not just preorder

[errant ridge]

ah okay

[neat lintel]

so yeah preorders are very natural very intuitive amazing things in mathematics

[errant ridge]

so with this kinda relation there'd be elements in the set that you can't compare?

[neat lintel]

there can be

we say x and y are incomparable when neither x<=y nor y<=x

[deep mango]

no idea. bot magic

[neat lintel]

its just a role it doesn't matter

[halcyon basin]

now i dont feel ashamed i need a calculator to do 8+7

for calculation

[errant ridge]

based

[errant ridge]

makes sense thanks

[neat lintel]

its not that hard, you just need a paper and a pen

and unrap the definitions of +, 8 and 7

[halcyon basin]

prove its not hard

rigorously

with theorems and proofs

[neat lintel]

hard is just an informal term here

the point is that all you have to do is unrap the definitions

[halcyon basin]

im just yanking your chain, I just have calculation paranoia

i have zero faith i know the numbers just off the top of my head

[errant ridge]

every pure mathematician does

[halcyon basin]

like if a test asked me 12 x 12

my mind says 144

[errant ridge]

144

[halcyon basin]

but id double check

[errant ridge]

yes

nah

I'd just write it

even if I knew I was wrong

[halcyon basin]

^different mindset

[errant ridge]

cuz that's just how i roll

[neat lintel]

8+7 = 8+succ(6) = succ(8+6) = succ(8+succ(5)) ... can you continue?

[halcyon basin]

imagine having confidence

smh

[errant ridge]

you gotta work for it

[halcyon basin]

well lets hope studying math will do that for me

because in school during math class i fell asleep

like a lot

[neat lintel]

do you sleep at night?

[halcyon basin]

I didnt get good sleep

[neat lintel]

you should see a doctor

[halcyon basin]

i was a stay up all night kind of guy

still kind of am

[tight comet]

if you don't sleep at night

[neat lintel]

you should get night school

[tight comet]

you should sleep more often

[halcyon basin]

i usually stay up all night , sleep during the day

if allowed to

[errant ridge]

I usually stay up all night and all day

I don't sleep

I'm on that sigma grind

[halcyon basin]

i think the longest ive gone without sleep is 2 days

surviving off raw willpower

[errant ridge]

the longest I've gone without sleep is my entire life

imagine sleeping, that's for the weak

[halcyon basin]

but yeah math has never been my go to subjects

those were usually reading and science class

funnily enough one of my favorite subjects in science was physics, though i doubt it will be in college

[errant ridge]

Lol it's even more fun in college

undergrad physics is the best

[halcyon basin]

but to me my brain sees math as random numbers, and then it enters sleep mode

thats been an issue

[errant ridge]

I think graduate physics will be even better

[errant ridge]

then you should do math during the night time so that you'll go to sleep

[halcyon basin]

mmm

maybe

i just wish i saw the beauty in math ppl like isaac newton, archimedes, etc. saw in it

[errant ridge]

watch 3b1b

[halcyon basin]

might give it a try

not sure any of these apply to me but i could check out linear algebra

[surreal sapphire]

archimedes

archimedes was really weird

he cared a lot about large numbers

[chilly hull]

archimedes when i show him rayo’s number

[neat lintel]

imagine if ZFC is not consistent. then rayo's number would be ill defined

more people should do googology on subsystems of second order arithmetic

[surreal sapphire]

hmm

archimedes also cared about diophantine equations

so he probably wouldnt like rayos number

i will ask him to compute the smallest integer solution to x^2 - 990676090995853870156271607886y^2 = 1

archimedes already knew that this has a solution

[grizzled grove]

hey Loch, I have a question about algebraic number field

[surreal sapphire]

you can try

[chilly hull]

y=0, x=+-1

[surreal sapphire]

ok this was my mistake

the smallest integers solution that is not trivial

[halcyon basin]

archimedes knew circles were the answer to infinite energy

[chilly hull]

😡

[grizzled grove]

It is regarding how many ideals in O_K have norm equal to n

[surreal sapphire]

lol

i asked exactly this question

[halcyon basin]

laugh now, but soon you'll see

[surreal sapphire]

some time ago

[halcyon basin]

maybe in a million years

you'll see

[surreal sapphire]

and merosity gave a good answer iirc

i only needed an upper bound

[grizzled grove]

well i need exact value

[surreal sapphire]

you can appeal to unique prime factorization

[grizzled grove]

upper bound is easy because of bound given by Landau

[surreal sapphire]

and then go from there?

[grizzled grove]

in UFD all ideals are principals and the norm =n for exactly one ideal, which is (n)?

i mean UFD+O_K structure is PID

[surreal sapphire]

you can factor any ideal into prime ideals

so start by counting prime ideals of a given norm?

any prime ideal lies over some prime number

so then you need to study the splitting of primes in your number field

for reference, this was the mathSE post where i got what i needed: https://math.stackexchange.com/questions/92426/how-many-elements-in-a-number-field-of-a-given-norm

[grizzled grove]

so a closed formula will depend on ramified, unramified and etc?

[surreal sapphire]

i only needed principal ideals and a rough bound

which i got in some comment

(i also needed it for non dedekind domains so the prime factroization approach didnt work)

[surreal sapphire]

i expect so

[halcyon basin]

your guy's appreciation for math both bores and impresses me

[surreal sapphire]

i think this can get very messy

[halcyon basin]

maybe its the entire day of sleep i dont have

that is making me tired

[surreal sapphire]

do you need a formula

you can probably throw together some sage code that computes it for specific values

[grizzled grove]

na i want to define something which requires me to use this function

which tells me number of ideals of norm n

what you shared is talking about number of elements of norm n

[surreal sapphire]

hm

i think you can instead count principal ideals of a given norm?

multiply your ideal with its inverse to get a principal ideal and look at how the norms relate 🤷

i dont really think a formula for this exists tbh

[grizzled grove]

i see. what you shared do have some closed formula for quadratic field

[surreal sapphire]

the only case that matters

[woven whale]

if $\infty^2 = \infty$

[fathom swallow]

illuminator3

[alpine kindle]

this depends on context

[woven whale]

$\frac{\infty^2}{\infty} = \frac{\infty}{\infty}$

[fathom swallow]

illuminator3

[woven whale]

$\infty = 1$

[fathom swallow]

illuminator3

[woven whale]

ok but now to be serious

I'm doing this recursive call

and I'm trying to unfold it

and I do $a - \infty - n$ for unfold $n$

[alpine kindle]

$\infty^2$ is not at all necessarily equal to $\infty$

[fathom swallow]

illuminator3

ally 🌈

[bright hill]

inf is not a real number

[woven whale]

wait no

$a - n\infty$

[storm sage]

infinity is just a symbol

[bright hill]

you can't expect non-real number to behave like real numbers

[fading tusk]

what do you mean a "real" number ?

[fathom swallow]

illuminator3

[alpine kindle]

oh my god please leave

[storm sage]

there are many ways in which mathematicians handle symbols

[woven whale]

it was a joke

[alpine kindle]

infinity can absolutely be a number

[woven whale]

can I just ask my actual question

[storm sage]

mathematicians define things that are useful

[fading tusk]

what is a number ?

[alpine kindle]

please all of you shut up

[bright hill]

I see

[storm sage]

ask not "what is this equal to", but "what contexts is it useful for this to be true"

okay I will shut up

[neat lintel]

you know you don't have to use the latex bot literally every time you want a math symbol, it just clogs the chat lol. you can just type \infty or ∞

[woven whale]

I do $a - n\infty$ (syntactic sugar for $\lim_{I \to \infty} a-nI$) in unfold $n$, if I want to indefinitely unfold my recursive definition, I'd need to do $\lim_{I \to \infty} a-I\infty$

[fathom swallow]

illuminator3

[woven whale]

that's where my $\infty^2$ comes from

[fathom swallow]

illuminator3

[tall badge]

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaAaaaaaaaaaaaaaaaaaaaaaa

[alpine kindle]

you can't define infinity as a divergent limit

[bright hill]

lmfaoooo

[alpine kindle]

divergent limits are undefined

[woven whale]

wdym

[alpine kindle]

lim n to infinity n is undefined

you'd have to redefine what a limit is for it to be defined

[woven whale]

well it's actually

$\lim_{\mathfrak{a}1 \to \infty} \smiley{}(\lim{\mathfrak{a}_2 \to \mathfrak{a}_1} \frownie{}(\mathfrak{a}_2))$

[peak tide]

depends on the context, in the extended reals it's perfectly well defined as +infinity

[woven whale]

wait

wrong one

[neat lintel]

god

[storm sage]

that mathfrak

LOL

I'm dying

[neat lintel]

this is one of the worst things i've read in a while

[alpine kindle]

ok what are f and g

[bright hill]

this is getting really silly

ally, mind if I help?

[storm sage]

at this point you might as well start using emojis as function names

[fading tusk]

what is wrong with the variables?

[fathom swallow]

illuminator3

[storm sage]

oh god

[alpine kindle]

no please don't

[storm sage]

it was a joke

[alpine kindle]

i don't want 1.noise 2.more suffering than my own

[neat lintel]

so territorial

[fading tusk]

you want some theorem for nested limits like that?

[fringe needle]

Is it just me or has illuminator been trolling simultaneously in two channels

[woven whale]

I'M NOT TROLLING I SWEAR 😭

[alpine kindle]

@woven whale how are you defining infinity

[bright hill]

sigh

sure

[woven whale]

IDK 😭

[alpine kindle]

and that is your problem

[fading tusk]

infinity can be defined in a number of ways

I prefer 3 different definitions at once

but no more

[errant ridge]

you used to have the active role no?

[alpine kindle]

every definition of infinity gets around your problem in a different way

[fringe needle]

It comes and goes

[errant ridge]

how so?

[neat lintel]

What don’t you tell them to go read analysis book instead of doing this

[fringe needle]

I’m active in bursts @errant ridge

[errant ridge]

ah okay

[fringe needle]

So if for a day I ask a few more questions it comes back

[alpine kindle]

analysis wouldn't help here

[woven whale]

'why don't you go read a book about english grammar'

[errant ridge]

lol i think i'm gonna be like that soon

[alpine kindle]

maybe a little

[woven whale]

see how toxic that is

[fringe needle]

I’d say I’m a relatively common user of the server though

[neat lintel]

Ok I will, now you do the same

[woven whale]

buy me one and I will

[alpine kindle]

aaaaaaaaaaaaaaa

stop

please

[woven whale]

how do you define infinity

what are the possibilities

[alpine kindle]

ok

I'll give you a few

the first one is to do with sizes of sets

[neat lintel]

the only good definition of infinity is as the north pole of the circle

[errant ridge]

the cardinality of the set of integers and the cardinality of the set of real numbers are two different sized infinities, the latter is bigger than the former

that's one possibility

[woven whale]

this is too many people talking at once

[errant ridge]

welcome to the math server

[storm sage]

EVERYONE SHUT UP BESIDES ALLY (and illuminator3)

[woven whale]

me included?

[vocal roost]

💀

[alpine kindle]

you can get infinite sets so you have to have infinite numbers to describe the number of elements in them
this gives you the aleph numbers

[woven whale]

OH

[alpine kindle]

thank you eric

[woven whale]

THAT'S HOW YOU SPELL IT

I ALWAYS THOUGHT IT'S ELEF

[alpine kindle]

yeah

[woven whale]

what are the other possibilities

[alpine kindle]

those infinities describe numbers of elements in sets
they extend the natural numbers so dividing them doesn't make sense

[alpine kindle]

you can have projective infinity, where you extend whatever space you're working on with a set of "points at infinity" of a dimension 1 lower than the base space

for example

the projective real line adds one point at infinity

[errant ridge]

does the riemann sphere count as an example of that?

[alpine kindle]

whereas the projective real plane adds a whole line at infinity

[alpine kindle]

yes

[woven whale]

base space?

[woven whale]

projective real line?

[tall badge]

idt we need all this to define lim=infty

[neat lintel]

isnt projective real line just a circle

[alpine kindle]

that means real line extended with points at infinity

[woven whale]

ah

base space?

[alpine kindle]

the space you're adding the points at infinity to

[fringe needle]

This is more the one point compactification than it is projective space

[woven whale]

in your sentence is "whatever space you're working on" and "base space" refering to the same thing?

[fringe needle]

For projective geometry, the “base space” is a vector space if you know what that is

[alpine kindle]

i mean the space you're working on is the projective space
the base one is the one you're working on without the points at infinity

[woven whale]

ah

[fringe needle]

But I agree with Roketto I feel like this is somewhat unnecessary to describe infinity in the context of limits

[alpine kindle]

they asked

[fringe needle]

Fair enough