#serious-discussion
1 messages · Page 4 of 1
Would you recommend any other stem servers?
John Cameron Urschel (born June 24, 1991) is a Canadian-American mathematician, former professional American football guard and center and chess player. He played college football at Penn State and was drafted by the Baltimore Ravens in the fifth round of the 2014 NFL Draft. Urschel played his entire NFL career with Baltimore before announcing h...
Just discovered this dude
Really incredible
PhD at MIT in math and a member of the IAS at princeton
Next week I'm going to start studying divisibility. Any recommendation?
have you seen this guy? https://en.m.wikipedia.org/wiki/Ronald_Graham
Ronald Lewis Graham (October 31, 1935 – July 6, 2020) was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He was president of both the American Mathematical Society and the Mathematical Association of America,...
Wait didn’t he make grahams number
was president of International Jugglers' Association and has an Erdös number of 1
Wow that’s insane
yes
he was friends with Erdös but unlike him he didn't forsake body for mind
That's a very nice way of putting what erdos did
he wanted to cut a grapefruit once but he used the dull part of the knife and as the juice shot across the room, Graham just cut it for him


Erdös wanted to drink grape juice at night but he couldn't find the cap in the container so he took a knife and stabbed a hole in it, this was while he was staying at Ronald Graham's house so Graham was woken up to that sound and had to fix it
Erdös was also once challenged by Graham to go up a down escalator and said "That's ridiculous, of course I can." So he took 4 steps and he fell over and slid down to the bottom as people were staring at him
Idk, mods seem to think its funny to rename their channels with higher numbers as if there are those many. shows how mature they are.
It’s kind of disappointing that so many of the established members in this community are nothing but trolls. For a server so focused on academic excellence, you’d think that these established members would be more respectful to and in the server.
Yeah that reminds me of how it’s kind of disappointing that so many of the established members in this community are nothing but trolls. For a server so focused on academic excellence, you’d think that these established members would be more respectful to and in the server.
It’s kind of disappointing that so many of the established members in this community are nothing but trolls. For a server so focused on academic excellence, you’d think that these established members would be more respectful to and in the server.
When I’m dreaming and I want a boring scene or a action directed scene how would I do it
Like to think about my math homework and know that I am solving it whilst dreaming about it
It's kind of disappointing that so many of the established server members in this community are nothing but trolls. I think why it produces so many gems and visionaries is because math is definitively hard, and has the hardest problems known to man, so men who consistently push themselves to solve adverse problems, will attain a generalizable ability to develop creative solutions to problems with ease as oppose to only dealing with the problems of a regular joe life, people who have been through it develop street smarts and learn how to solve street problems, but you can only see so many street problems, there are thousands of math problems in physics engineering and many other disciplines it is pure beauty!
It's kind of disappointing that so many of the established server members in this community are nothing but trolls. I think why it produces so many gems and visionaries is because math is definitively hard, and has the hardest problems known to man, so men who consistently push themselves to solve adverse problems, will attain a generalizable ability to develop creative solutions to problems with ease as oppose to only dealing with the problems of a regular joe life, people who have been through it develop street smarts and learn how to solve street problems, but you can only see so many street problems, there are thousands of math problems in physics engineering and many other disciplines it is pure beauty!
Is that a copy pasta
LMAO literally
Fuck off cliche boy
men
Also don’t shitpost my shitpost, it’s disrespectful
Good morning cranky
Rycie
I stayed up almost all night last night because my fucking cpp wouldn’t compile
And I finally got it to compile
So cringe, use a real language
And now I’m getting fucking segfaults
LOL
It’s for an assignment
No one calls it cpp
And every function name is like 3 lines and it’s a nightmare to find the actual name in all the scoping and datatypes
It’s easier to type cpp than c++ on mobile
Are you sure widdle baby doesnt need valgrind?
I use gdb ryc
I’m a big boy now
I’ve graduated from valgrind
I’ll use valgrind afterward to find my memory leaks. Right now I want to get the program to work
Soon you will graduate again to julia
If my course accepted other languages I would not be using cpp
Wow. Where did all that big talk go
Use prolog instead 
What big talk
Anyway I dont have time for schnee esh. Big brother is popping off tonight
About using fucking gdb?
That’s big talk to you?
I was literally complaining about cpp ryc
No about how C is the optimal language and C++ is gonna be your next foray
Smh “gem”
Or whatever
Oh
No
I said I was slowly warming up to Cpp but I still didn’t like it
I liked writing cpp I don’t like compiling it
I put that through the slurp -> normal language translator
Also I used to be good enough at C to not have to worry too much about segfaults
And it parsed as "I really like this thing but im too tsundere to admit it"
I speak normal language!!!!!!
My bad if that was misparsed
That’s actually valid ryc
But no
I came into this course with high hopes for cpp
Turns out it’s shit
Anyway I’m gonna go bother some people with some questions
Have fun
Hope your day is productive
I hope so too
Have me with some sea turtles to make you feel better
OMGG
I LOVE SEA TURTLES
This is you?
Yes
Ew
Sea turtle is to my left
Yessir
Below me is my colleague
But that’s actually sick
And to the right of me is some dipshit
I bet it was really dumb
And it was dead
Oh
LOL
Yeah, dumb as heck
Circle of life brodie
Oh bullshit
Ugh that was disgusting to type
It probably died from plastic
I vaguely remember seeing plastic around it, I don’t know if that’s what killed it though
There was no plastic in sight around these guys, which is nice

I'm just going to go with the interpretation that you want to suffocate me with a grocery bag
That's about the most charitable one I can give
Unless you were thinking bubble boy
It wasn’t a weird thing to say
That movie
Ok
It’s kind of disappointing that so many of the established members in this community are nothing but trolls. For a server so focused on academic excellence, you’d think that these established members would be more respectful to and in the server.
Good morning shyshy
It is good
I gave my talk
It was good
Tomorrow is the last day
I am very very well liked here
Like
Really??
Good morning slurp
Well
Its better than sitting there and saying nothing
No ryc
Even if you are confused
That’s exactly what I would do
Yes
But I wouldn’t be confused
And its what i did for the last year
Which was silly
Why
Im not actually confused
Like
Sometimes I get confused and then figure it out
Sometimes i think they're wrong
And then I act like im confused
Good to hear
Instead of saying "thats wrong"
Oh
Yeah makes sense
Hmm borING
And i like presenting the solutions
Ugh
It's fun
I am very outgoing
Exactly
And it's partially to piss you people off
I bet you’re the kind of person who starts conversations with random people just for the sake of it
Yes rycie?
I was so sad during my italy switzerland trip cause i kept wanting to do that and i only did it like twice
I wanted to do it like 20 times
WTF
I just couldnt get myself to
You’re so weird
But here I've done it like 10 times
Hey ryc remember how you forgot your chocolate??? LOLOLOLOL
Its so good
I feel like you and my brother would get along well
Im not even going to engage with that
You’re both weird in the same way it seems
I'm the oldest of 3 brothers, and I exude that
I’m literally a middle child
I drip middle child vibes
Its one or the other
Only children are not as cool and independent as I am
Yes
Makes sense how you’re able to put up with me then ig
You’re… 23 right
Oh you’re also the same age as my brother
24 in a few months, a real age finally
Wow you guys would get along
Is he hot
Good thing you live across the world from one another
You two together would piss me off
You’d like
Echo off one another
Are they like mini jesuses?
Wtf
Ugh
You’re a family of weird hairs
I have normal hair because I’m a normal person
What does weird hairs mean
Yours
My middle brother doesnt have weird hair
Yeah okay
My parents dont have weird hair
I think he just has it because of me
2/3 majority rules. By the transitive property your middle bro has weird hair
That would make sense yeah
I’d also want to be exactly like you
Is he also weird about math?
Do you want to be exactly like your brother?
No
My brother is a computer nerd
I tolerate computers
rycc
Fuck off valley
Fuck OFFFF
Actually good that you’re here I need to start my day
Go talk with rycie valley
awww is slurpy wurpy mad
ew
One of them is your age
ryc is so old
You’re 17 right
i’m seventeen
AYO
14 15 about
Kithes!
EAT SHIT
why
Shit isn’t tasty valley.
oh
What a silly thing to suggest.
It’s kind of disappointing that so many of the established members in this community are nothing but trolls. For a server so focused on academic excellence, you’d think that these established members would be more respectful to and in the server.
Bye
how do you know
Guess
i didn’t knowi was an established member of the server
you fell down and some just happened to get in ur mouth?
bro do something impressive i’ll praise you pinkie promise
😂 😂
you’re the one who ignored me 🥰
https://www.alltrails.com/trail/hawaii/hawaii/mauna-kea-humuula-trail
Read the reviews and weep
Everyone agrees its fucking hellish
reviews from weak people
We met a dude on the trail who was coming back
He turned back after 2 miles
We got to the TOP
I dont need praise
i am so proud
Your pride is an insult
” ryc try not to lie challenge (IMPOSSIBLE!!! COLORIZED!!)”
I am a skilled liar
that sounds like something a liar would say
A good liar knows that getting caught in a small lie and owning up to it effectively can mask a big lie
Hi [ \mathbb{Chalk} \mathscr{RYC} ]
Hi grass
grass
” no it really *was * three minutes it wasn’t TWO!!” - ryc

The hike took us from 10:30 am to 7pm
liaryc

DOOT

wsp
Kinda late here
yee 2:38
Only 12:38 here lol
hell na
today is not a sleep day
Cause i wake up every morning feeling so gross
one of my friends sent me a suicide note
Could it be a humidity thing?
Oh! That is crazy
Oh that's fucked
hes fine
Dont sleep then

i called the police
Good
I am about to stick something up my nose
abt
tfw ryc exposes all his professors to covid
Could be some new disease
calling it rn
sharkpox
we can name it after him
Here are some cool pictures
first pic is awesome
did u have fun
was it worth it?
The feeling of catharsis of cresting that view with the observatories
Was really really good
Very much so!
Oh also
Since we got back at sunset
We waited around a bit to see the stars
And you could see the milky way really clearly
Time to wait 15 minutes to see if another line magically shows up on this covid test
(it wont)
Annoying
Did you see the sea turtle pic from before valley
We were also at this cool beach
And this crazy valley and this 450 foot waterfall
So
Good stuff
touch that grass
Here's a cool gecko on a weird flower
yes i did it was nice i love turtles
valleys 🥰🥰
Yes
12/10’ gecko
Yes
It is a nice experience
Thank you for your compliments on my pictures, this phone camera always surprises me

this is a safe space from #discussion

Lol
is anyone here comfortable with dimensional analysis :)
In physics?
Alright I can help ig

Even shy lol
Cool, are you familiar with buckingham's pi theorem
Okay sorry I can't help
Ah ok
has nothing to do with pi he just decided to name his variables that
lol
i am reading its wiki page
this seems like its a bit above what i know
by a bit i mean a fair amount 
wikipedia makes everything too complicated
I thought the question could be related something to units and dimensions 
it is ! !
Oooh
if u want the question its here
i just wondered if anyone else here cared to try so i could compare an answer
i got it from a very brief physics course and im not rly in contact with anyone else that attended
Ooh
JellyShark
once you get a formula the dimensional analysis part of the question isnt too difficult. If you dont know the poiseuille flow equation by heart you can rederive it from navier stokes by taking the boundary conditions u=0 on the boundary of the pipe, getting an explicit formula for u (it's a degree 2 polynomial in terms of the distance to the boundary), and then integrating to get the volume output
or use the formula given by JellyShark straight away (im not sure the 128 is completely correct though 🤔 ? Idk i never remember the formula by heart)
i look up from Wikipedia though
buy yeah, relationship of units can be inferred from the quantities themselves
viscosity is in $[Pa\cdot s],\ P/l[Pa/m], d[m]$
to get $Q[m^3/s]$, Consider $\frac{ΔP/l\cdot d^4}{μ}$ we can get the units to be $[Pa/m\cdot m^4/ Pa\cdot s]=[m^3/s]$
so you can infer the what will the factors of Q change by this relationship
Oh that's what i got!
Nice!
My friend asked me about this puzzle (See if you can solve it!)
11223 = 0
786 = 3
1947 = 1
then find the value of 2983
It is spam lmao
you don't know how to treat with math (I think)
how to what


Im not sullying you
it's an interesting problem btw
Yeah I liked it
im not sullying u either lolz
for example |x+10|>4*|x+3|
its same as x+10>4*|-x-3|?
is that right ?
are they the same?
Sullyception
@neat lintel spam and puzzle aren't mutually exclusive, general rule on this server is don't multipost
the venn diagram of puzzles and spam has nonempty intersection
how did you get that
they do happen to be the same
you should move to a help room
but I'm confused on how you got there lol
if youre going to answer these kinds of questions
All mathematical research is a form of spam chain mail
"Think about this unsolved problem and publish an article on it within five years or your career will suffer."
omg that reminds me of that one "get me off your mailing list" paper
I'm not aware of this? 
I think I've seen this one before 
help channels kinda slow today
why are you on the help channels
who cares
which is obviously unacceptable
Give money to discord or something
I was considering getting nitro, they do have that promotion going
at least I think they do still
why not? Its a good platform imo
hahahahahahahahahahahahahahahahahahahaha
what dont i know 
discord is made by a bunch of middle aged furries who spend all their time jacking off to cub porn instead of fixing issues with their app and adding qol things that anyone who has ever used discord in their life would ask for
dont waste money on nitro
LOL
admittedly
with the furry icon lmao
exposed
i forgot i even had a nitro subscription. i just cancelled it
like what qol changes?
:O
they only recently added muting
I wish all the notification settings were in one place, but thats about it
something everyone has asked for forever
they are actually
muting other ppl? like in vc?
The only thing I see nitro used for is for using emotes from other servers
yeah
bell icon in top right has all your notifs
wait oops
i don't want to see messages from people i've blocked, i don't want to automatically ping people on reply, i want embeds to work more than half the time
i mean the inbox one
^^
next to the ? button
i don't see the reason for having a "servers joined" limit
you can right-click the server icon to see some, you can click the dropdown at the name of the server to see others, then you have the channel by channel settings
i didnt even know there was one, how many is it?
100
yeah you mean like the grey bar or whatever popping up? That is annoying
the automatic ping thing makes sense too
auto off makes more sense
i've blocked a lot of people on this server and it makes reading through some channels very painful
lol
100 servers isnt enough?? dang my mans
i think the server join limit is an infrastructural, in the sense that someone could join 200000 servers and then determining when they're pinged is really awkward
tterra's patience is like zero
but i dont see why its 100 instead of like
idk, 250
like 100 is more than enough for me but ive heard of people hitting it
so
I know people
all the discord creators like to do is rip off slack
I’m probably close tbh
first replies, then threads
i'm in 12 and i only interact with people in like 3 of them
i get annoyed when im in more than 20 and gotta do a clense
soon discord will be exactly like slack
discord was created before slack
Mostly because I’m too lazy to leave servers I’m inactive in
iirc
yea but threads/replies were on slack long before discord
i use folders to hide servers i don't want to be shown in screenshots
LOL
Have you looked into betterdiscord?
rokabe mentioned it to me
isnt that bannable
technically but nobdy cares
idk if anyone actually gets banned for using it though
i don't use discord to DM people so i don't really care if i get banned
you should get betterdiscord its pretty cool
Discord devs said something about that themselves
i'm not attached to anything on this account
That they don’t care or something
i might get it then
other than me 🥰
i dont want to get banned because I dont want to have to find server invite links again
Don’t take my words for granted
yeah ill check first
fuck
I might be misremembering
there's probably info on the better discord page if they have
just go to all your servers, generate a non expiring link and paste them all on a google doc
but honestly i guarantee you're not gonna get banned for using betterdiscord
It seems like betterdiscord is against ToS, so technically it’s bannable, but I don’t think Discord can be bothered to ban everyone using it
literal pedos on discord dont get banned
also i use my personal server as a storage device lmao
well yeah, you think discord admins are going to ban their fellow admins?
Wow
hi slorpy
Discussion is heating up
Hi moddy!
one of my TAs from undergrad had office hours on discord
if anyone from any of my classes saw anything on my discord account i would want to drop out
it was pretty cool actually, having the organizational structure for course items. also there are better options though
canvas does suck
if i were in sketchy servers id be afraid of someone clicking my name and seeing it in common servers
not that i am or anything
Tbh the biggest issue I’d have with using discord for class is that I’d shitpost way too hard
non axiom of choice servers
And then the prof bans me or something for disrupting everything
that's the risk they accept by using discord as a medium
the good thing is that the overlap between this/other normal servers i'm in, and the sketchy servers i'm in, is empty
that's impressive
I like how you consider this a normal server
compared to the other ones? it is
i feel like there is at least 50 furries in this discord, for exampel
lol
wat
lmao
maybe he has you blocked lmao

i would block me too
i don't have namington blocked
lmao
mutual server is not a symmetric relation, obviously
challenge: describe gmod in 4 words
how to get banned speedrun
you're in a math server my guy
Lmfao
lmao
I dont think ive posted anything here that I would be embarrassed for my academic advisor to see
memes, blue, maybe undergrad?
what if your advisor saw the math discord wiki
theres a math discord wiki?
That is some of the stuff that would be closer to being embarrassing, yes
What about the feet pics
what about when you were talking about hot guys in chill
Hi all! I'm new to graduate school. My name is ranya kumoschalkboard but you can call me RYC for short (pronounced "reek"). I love egg bagels, four cheese pasta, and taking short walks by the beach. Excited to meet you all!
Thats fine
Idk I saw some #feet-pic meme in some pin I think

I WANT FEET PIICSSSS
LOL UR JOKING
I’ve joined a few times
It’s pretty fun
i am a goblin
Yummy
wait @deep mango did u have another account
bc I looked at your first message and it was not that long ago
also looks like people already knew you
im pretty sure all the mods are the same person with like 10 different VMs
LMAO
I joined like a little more than a year ago
I am ryc’s alt
whomst?
Angetenar the tex man
Ryc being cringe?
LMAO
Holy fuck I’m tired I literally cannot figure out what ryc wrote in these messages
its hard to understand things without context
something something the dress is blue and black
it's orange and gray
No man
ive never known someone I liked and also saw gold and white
lol
serious question, pi or tau?
pi
agreed
cmon man everyone loves the pie jokes
my take on the whole tau thing is it's stupid to define a separate constant for 2π, but it's maybe not so stupid to define a separate constant for 2πi
even high schoolers
elementary meaning less experienced than I am, which is an incredible and very objective metric
Pi isn’t a consrant over the rationals t ro ll
what
I sometimes use pi as a variable in my own work lo
cursed
Pi is used for a lot
pi is typical for permutation
Counting functions, projections, etc
Homotopy groups
piece of pie
Vector bundles 
projections
I prefer cake
prime counting function
lie groups are great
interesting?
I like their name, good meme potential
what do you mean by opinion on a topic
Lie groups are a nice example of spaces that have global frames
discussion starter
wait, people use anything other than sigma for permutations?
lol
damn
wtf is that
I looked at those as examples for my oral exam
polyamory flag
why twice tho
what does the poly flag have a pi in it
lol
pioly
they really could've toned down the colours there
They did
yeah that hurts the eyes
So true
what in the world
physicist move
have I explained the double epsilon strat here? I don't think so.
Have you ever wanted to say $x \in U$, for some $U \subset M$? Instead, imagine $x \in \in M$! It's the perfect solution
Migillope
Heyyyy that's cool
the unique quantifier extends nicely too
whats wrong with $x \in U \subset M$? or am i missing a joke
ΣAC
Is that double epsilon useful when U is unnecessary?
like i don't care which subset of $M$ that $x$ is in, so $x \in \in M$
riemann
thats pretty neat
so its shorthand for "x is in some arbitrary subset of M that i dont care to name"?
oof don't use this notation
or group of groups
in what instance would you need to talk about an element being in a substructure but never need to reference that substructure?
basically never
$x\varepsilon\bR$
its especially good when you accidently write on a chalk board \in when you mean \in U \subset M, and dont want to erase
since like, x in U contained in X with U unspecified is literally equivalent to x in X
>>> riemann.dadjokes()
OverflowError: math range error

If U is a subset of X, then by definition if x is in U x is in X
yeah
2 is in an element of the power set of naturals, but 2 is not in the power set of naturals
{2} is
"x is an element of some unspecified subset" conveys no additional information
not 2
In your notation above you have U subset X, not U in X
set theory is a bruh moment
$2 \in {2, 3 ,4} \subset 2^\mathbb{N}$, $2 \not\in 2^\mathbb{N}$
anyways this is silly
Migillope
But
no that would be {{2,3,4 }}
set theory enthusiasts really be like "1 is an element of 2"
Yeah
or just double epsilon which instead means x \in U \in M
which is actually what I wanted it to mean in the first place
the other would be \in \subset I guess
yeah
they look the same
if you dont look too closely
Was that in intentional?
I don't think "element" and "epsilon" is a coincidence
Mmm
also like, before latex
it was convenient to typeset \in as \epsilon
since some typewriters had this
the symbols are slightly different, but I don't think they are related, are they?
no no they are related
they are? Whats the history there
epsilon = small, \in = smaller than so that it can be in?
Ah Wikipedia says they’re related
historically \in was \epsilon
now it's used commonly enough that it's useful to have like
\in is a perfect symbol
a distinguished stylized version of it
Ooo that makes sense
especially so as not to conflict with greek letters
I read that and im like "yeah that means in"
but you can imagine how this happened like
where did the inequalities come from
Work out my problems guys
hmmm I need a letter for a relation that means "is an element of"
#❓how-to-get-help , or more likely #chill
for what reason?

I guess ≤ and ≥ are pretty natural because if you want to modify = to have some directionality
this is a pretty minimal way to do this
Oh that’s cool
though what's not clear is like
why was one direction chosen over another
like why does > mean greater than and not less than
that's purely convention
perhaps element?
because the big end points to the bigger one
It’s the Pac-Man
Or is it the crocodile…
i saw this without context and i thought it was some kind of wierd trigonometric proof or something
Crocodile eats bigger value
and bird eats smaller, is what I was told once
anyone here majoring in cs?
Go gators!
Go gators!
😶🌫️
Is it alright to ping someone to ask them a question?
Nvm I go for it. Sorry @neat lintel for the ping but can you post the link to your course website for linear algebra 1 and 2. I want to follow the homework list
Sorry again for the ping
linear algebra 1 had no course website, and you can find linear algebra 2's website in my DM history
Thanks
Lmaooo same
Wow got spooked by my own pfp
There are cosmic snipers firing at random into the universe. What are they and what happens if they hit us?
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Spanish Channel: https://kgs.link/youtubeES
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This is how we make our living and it would be a pleasu...
3:54 “any more detail would require more mathematics that necessary for a youtube video”
What kind of mathematics is being talked about?
And what kind of physics?
What does one google?
seems its referring to gamma ray bursts? if so, thats solidly more of a physics topic
oh of course it is, that's literally the title
kurzgesagt usually put their sources in the description
very studious for a calendar cult
You’re definitely part of said calendar cult
the part before it says about how GRBs stay focused and don't fade, so they can be seen further. Sounds like optics to me; electromagnetism and optics
Kurzgesagt!!!!
This is the closest you’ve come to actually offending me
Yeah that was too far, I sincerely apologize.
What is displacement and how can you change what you see from objects to action potentials through object/action deep backpropagation
Should I take notes when reading math textbooks? I often try to take notes but end up just copying the entire textbook.
have you tried putting it in your own words?
I have, but l just find the author's words more elegant and sometimes copy them.
Maybe I should try writing the proofs without looking at the proof and do it as en exercise.
probably a good idea
i would think that a memory would be easier to build if was a "sentence" similar to one your mind makes naturally, y'know
probably
that makes sense
what I might try may be to do some reading first and then trying to prove the theorems by myself an hour or so later, with my own words
let's see how that turns out
I generally only take notes on things that are not in the book
intuitions, quesitons, ideas
references to compare with
etc
If you want to learn by writing nice notes in your own words, this is sort of a separate project imo
and is usually best done in hindsight
I don't think I've reached the point of comparing the textbook with other references, though I am also using another book. I do plan on writing on a separate notebook some intuitions, questions and ideas I may have.
Thanks for the advice
That's why I want to do it as an exercise only after the reading.
what does “sub-K algebra” mean in this case
Does this mean every algebra on the vector space of L over K
Just asking for a simple clarification on a term
also I was gonna start conversation off of that
well, I would assume this means that all sub algebras of L that're K-algebras happen to be fields
”sub” algebra?
i originally interpreted this as every algebra over the L-K vector space is a division algebra
L is a K-algebra, a subalgebra of L is a subspace of L also closed under the multiplication operation
A h
I should point out that I'm only using "subspace" in this context because K is a field, I guess more generally if you have an algebra A over a ring R, a subalgebra B of A is a subring of A that is closed under the action of R
same thing really but this feels more natural to me for some reason. The first definition I gave is "subspace closed under ring mutiplication" and the second is "subring closed under scalar multiplication"
A vector space is kind of a field of scalars with a vector abelian group (s o r t a like a group action) but like, if L is a K-algebra, what is the vector abelian group, and what are the scalars. Is the underlying vector group some set of elements of L
actually nvm
awesome conversation
was gonna be something else; got distracted lol
it just feels weird for the vector group to he an additive supergroup of the scalar field’s additive group





