#serious-discussion
1 messages · Page 47 of 1
i think u broke em zorn
it's the limit of x^2+3x+2/x^2−1 when x goes to infinity
I broke your mom
Does that mean he's coming back from the gas station sometime soon?
that’s not really that much i would say
i have like 500 hours on a game i’ve played for like 5 months
thats good
This is a short, animated visual proof of the two-dimensional Cauchy-Schwarz inequality (sometimes called Cauchy–Bunyakovsky–Schwarz inequality) using the Side-angle-side formula for the area of a parallelogram. #math #inequality #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #algebra #areas #mathema...
the music is making me fucking lose it
"free clash of clans gems (WORKING 2012)" type beat
neat video, but yeah the music just completely ruins it
Does x^2 count as a variable
yes
x^2 + x^4 is a quadratic polynomial in terms of x^2, because by substitution t = x^2 you can see it's equivalent to t + t^2
Never let your son choose the music
I'd like to clarify that by "making me fucking lose it" I meant trying to hold in a laugh at the library
I have never been more engaged with studying, hats off to his son
ain't no way that music ain't ironic loooool. I think dude like just made this video and then for music he just wanted to show off what music he listens to because if you don't like it seems you can mute it without losing anything
sometimes when I make videos on YouTube demoing some program I coded I leave my music running in the background if I know it won't be copyrighted
Content is fine tbh
Loool
Hi ricey
Hello grass
Two of my books will be arriving in two weeks time 
Then my copy of Schroder is gonna come late jan
Exciting
I see
dopium
has anyone else in here tried to talk with chatgpt about math?
As an artificial intelligence, I do not have the ability to participate in online communities or join Discord servers. However, I am able to answer questions about math and provide information and explanations on a wide range of mathematical concepts. If you have a specific question about math that you would like to ask me, I would be happy to try to help. Just let me know what you would like to know, and I will do my best to provide a helpful and accurate response.
While it can be helpful to ask for help when you are struggling with a math problem or concept, it is also important to try to work through problems and challenges on your own as much as possible. This can help you to develop your problem-solving skills and deepen your understanding of the material.
Can chatgpt do TeX?
Sure
humanity has been working on it for 40 years, I only know how to prove a sqrt log bound
now tell me fake AI
what is the answer
Xan has left us. Chatgpt is dead.
chatgpt is alive and well
it's currently trying to give me an asymptotic bound for the expected injective norm of a gaussian tensor
yesn't. It provides a proof, but sometimes the proof is inacurrate lmao
No
a bit lengthy answer

I meant a list like in programming
Indexable etc
Okay how about a macro which gets the length of a string?
See how it can fuck that one up
you know, I'm somehow more impressed by the fact that the AI produces me wrong proofs instead of saying it doesn't know.
I had to do some conversation with it first
\newcommand{\mystringlength}[1]{%
\countchars{#1}%
}
\newcommand{\countchars}[1]{%
\countcharshelp{#1}\0
}
\newcommand{\countcharshelp}[1]{%
\ifx\0#1\relax\else\advance\mycharcount 1\countcharshelp\fi
}
\newcount\mycharcount
Omg
Bruh the math people not even helping
I'm on my phone and too lazy to copy the whole answer
Do it yourself smh
It is entertaining though
Yeah it doesn't work, but it is close
\newcommand{\mystringlength}[1]{%
\countchars{#1}%
}
\newcommand{\countchars}[1]{%
\countcharshelp#1\0
}
\newcommand{\countcharshelp}[1]{%
\ifx\0#1\let\next=\relax\else\def\next{\advance\mycharcount 1\countcharshelp}\fi\next
}
\newcount\mycharcount
\mystringlength{hello}
\the\mycharcount

The package provides a large and sundry set of macros for the manipulation of strings. The macros are developed not merely for cosmetic application (such as changing the case of letters and string substitution), but also for programming applications such as character look-ahead, argument parsing, conditional tests on various string conditions, etc. The macros were designed all to be expandable (note that things such as \uppercase and \lowercase are not expandable), so that the macros may be strung together sequentially and nested (after a fashion) to achieve rather complex manipulations.
Sources: /macros/latex/contrib/stringstrings
Documentation: README, Package documentation
Version: 1.24
Contained in: TeX Live as stringstrings, MiKTeX as stringstrings
Topics: Text manip
See also: getargs
Read more at CTAN page of the package.
Got that right too
A bit unbelievable and eerie
Yeah it's really cool how accurate it is
Also why was it so sudden?
There was no buildup, they just released chatgpt one day it seems
It will turn out that technology is already that advanced and half of the people here are AIs
Beep boop?
what a casual scrub smh, artificial intelligence, more like artificial stupidity amirite?
@neat frost btw it doesn't only speak English, any questions you have in your language?
English is my language 
...ok
I see
Just a typo dw
ChatGPT should make more typos to pass the Turing test
hebrew?
it just generally became totally incoherent
Fucking lame answer Wtff
Indonesian, but I feel more comfortable with German
No idea what you're talking about
The answer is like "yeah I can't give you an answer. I am mashin."
And what were you asking?
Its thoughts on our current government
Oh lmao
It rarely has an opinion, but if you ask it what a certain kind of person would think about it, then it'll give better answers I think
I have no strong feelings on them
Please laugh
is a better reaction than a laugh
Oh is this an opinion of yours?
Anyone can get a laugh, it takes someone truly special to get a 
Pathetic. Smh.
No it's a fact
That sounds like an opinion to me
Noooo nnooooo 
Not me. I'm the goat.
Does it? I get them all the time
Lmao
what's the general consensus on self promo here? I wanna share my math stream here but don't wanna push on any rules/be annoying
I hate unopinionated people so much
I don't really have an opinion on opinionated people
lol
Opinionated people are good iff they agree with me
The help channels are bopping up and down and disappearing when I select one. Is everyone experiencing this? Makes it hard to keep track of which I've checked to see, if my skillset fits
You can always use #1021175428326633542 and check those
Oh thought that was the category name for the help channels
Haven't seen that discord function before
The category name for the occupied help channels is help channels occupied or something like that

rak bib
chm nky
chm nky
chm nky
Hi C-monke
Hi Kirb
rak bib
Hi grass
Hi kirby
Flandre Scarlet
I wish I could have found a Flandre fumo
I found a Reimu one tho
So worth it anyway
If you camp amiami.com, you’ll probably be able to find one for not hundreds of dollars
I shall not spend so much money
Does mosque = masjid
Ok
Mosques all face towards Mecca right
And the mosque in Mecca faces towards Medina?
Or Jerusalem
Oh sure
But don’t they have the wall nook inside that shows which direction

Enderton is my introduction to Algebra 
Why is there a theorem 5ZG
Knowing when it doesn't know something would be very impressive
Means it can monitor itself for truthiness somehoe
Oh that's because for this particular chapter (chapter 5), the Z here represents the section on (constructing) integers. While the G here is the theorem numbering for this section on integers. So, Theorem 5ZG means the 7th theorem in the section of integers in chapter 5.
In other chapters idt there's this 'intermediary alphabet'
this is weird notation
Perhaps why the author went with this here is because there are like 33 theorems in this chapter and there aren't enough alphabets. Or he thinks its easier to reference with that 'intermediary alphabet'.

Well, i was just joking anyways haha. I'm going read Jacobson's Basic Algebra I when I want to learn Algebra
Just out of curiosity, what's particularly weird 
please ping me when replying to my messages

S¹
T
Sorry, but upon close inspection, this differs from a circle by 0.2%
If you could only take two additional classes after a first semester in analysis and a first semester in abstract algebra, which two courses would best prepare you to self study more math in the future
Have you done linear algebra
Hmmm
It depends on what sort of analysis class it was
But I'm tempted to say a topology class
Pointset topology for sure. After that, it depends; if you want to do more analysis take something analytical, if you want to do more algebra take something algebraic. If your school has "Analysis II" or "Algebra II", both of those are good ideas.
One of my big regrets is that I haven't been able to take a complex analysis class, because that's useful and comes up all over the place. So maybe consider taking complex, if your school offers it?
One of my big regrets is that I haven't been able to take a measure theory class because that's useful and comes up almost everywhere.

Wanna do measure theory together? 
Sure, that's something I would do more seriously than cat theory or algebra lmao
surpass slurp
?
ah
do you have a recommendation btw? there are lots of measure theory texts
alright
that's a well-liked one
The last chapter of Rudin PMA
ok thanks
Then start reading books that already assume a knowledge of measure theory and sort of pick it up as you go
That's how I did it
I kinda already know some of the results in introductory measure theory (Caratheodory, monotone convergence theorem, dominated convergence theorem)
I just lack a lot of confidence because I never did the proofs and exercises
What text did you learn those results in? You can try to do the exercises from that text to build up confidence
recaps in differential geometry texts 
Oh well then I can't help you that's basically what I did too
(not diff geo, but recaps in other texts)

I see
rudin PMA measure theory chapter is notoriously bad
folland does stuff in generality and does it in the correct order IMO
I had to think twice whether zorn was serious or not
my math exam is 100/92 😄
\pagenumbering{gobble}
Latex moment
Yeah that was my joke
XanTeX will be born soon
Also turns out there's a major bug with my package 👀
yes
I gave you the benefit of the doubt 
contents of folland
LOL
(this is loss)
How are you with physics?
Tbh I'd be willing to try out XanTeX
good/bad
not very good? i only know bits and pieces of physics
Is that when you do a bunch of xanax and try to type something in latex?
Nothing to be ashamed about
Just about yeah
Good morning SLurp
Shall I show you the exam question in Turkey?
thanksie
university exam
Sure
ok
i translate english ok ?
Ok
We're learning about skeletons in image processing
or math no problem
Spookie scary
built-in package for better 3D visualization than tikz / pgfplots
Gross who's gonna be willing to implement that shit
look at him
Pinned in #latex-help
lol
his hair is so perfect all the time
Leslie Xanport
yuck
Fugly
hard or easy
Noice yohan of your mom
I at the very least hope you know who Leslie Lamport is

Also a woman's name
To Jill:
For your books and brochures.
Wtf
I added all those spaces and I removed them
nope, he's perfect
No he's unironically very fugly
wrong
Bad taste ryc
you don't get it
Correct
He looks like the sort of guy who either doesn't do drugs, or who does a lot of drugs, and either way it's a large part of his personality.
umm hard to tell but from how he was on the show i'd guess a lot of drugs
Yeah that makes sense, from the two pictures of him I've seen
He also looks like a devout Christian who is simultaneously super into new age stuff
So a lot less like a hippie
a lot less a lot of things, but mostly just a lot less hot
Does his dad own a boat?
Because in that last picture from before the game he looks like the kind of guy who always talks about how his dad owns a boat
so he's probably wealthy
are you seriously reading the tex book
A texnician
a texromancer
@broken crown ryc is trying to steal your thing
Oh whoops that was a different JohnDS
Lol
I actually remember when that other JohnDS joined the server. It was weird
The first few chapters are not interesting ofc
And a very quick read
Chapter 7 is probably where things become interesting
This is intended for people who have never used TeX before
So ofc the first chapters are about the basics
Takes a few chapters to get into depth
skip the texbook, just attend Xlurp's talk
Yo guys, I wanna hear ur answers to this, everybody says something different, so that kind of made me curious
What is the correct order of the following words:
( result / hypothesis / observation / question / curiosity / experiment )
alphabetical
lexicographical
No, logically, I mean what is the first thing that leads to the next. They all agreed that the result is the last, but they differ in the firsts order
BTW i think that's: (observation / question / curiosity / hypothesis / experiment / result )
Like , Doesn't it make sense?
Curiosity -> Question -> Hypothesis -> Experiment -> Observation -> Result
I would put them like this
Why
Scientific method I guess
yeah this seems vague and overly prescriptive but
if i were to answer this assuming it was a weird high school question
i'd answer what beijing did
I don't think it makes sense to just be curious like that
Sometimes you are
You will notice something first
Also you could notice something, but not be curious about it and ignore it. So Curiosity is what matters as first step
you start with "curiosity", i.e. wanting to learn about some phenomenon or whatever — as you focus and refine, you "narrow in" your specific interests and formalize them as a question
But wait
observation always appears at the experimentation stage but not necessarily at the first stage
"an observation" in a scientific sense is a specific measured outcome of a trial (i.e. part of an experiment)
scientific experimentation is the process of collecting observations
admittedly tho not all of the terms used are scientific in the first place, i have no clue wtf "curiosity" means
but it seems like this was structured as a way to basicall ytell students
hii
"to start researching things, first you have to take your general interest in the topic and formulate it into a specific, answerable question"
so im assuming they want curiosity to go before question to reflect this
Isaac Newton was not curious about gravity at all, when he noticed the fall of the apple and said why did it fall, he became curious and began to give his looks and research and gave experiments and then came to a conclusion
He wasn't curious and then asked
The people I think about are more like Francis Bacon and Galileo when it comes to Scientific Method theory.
newtonian gravity came as an attempt to explain the orbit of celestial bodies
i.e. the planets and moons
He was not curious, then he asked to notice something. When he thought with himself or asked himself, he became interested and curious
You cant be curious out of nowhere
in any case, my point is that i think youre misinterpreting what "observation" means
in the context of a scientific experiment, an observation is a specific element (a quantity, a phenomenon, whatever) observed during the experiment
not something observed before the experiment
The teacher said that by observation we mean the first thing we see apart from experience
So I said it's the first
alright sure
i can see that then
but thats not the definition of "observation" i'd use
when i hear "observation" wrt science, the first thing that comes to mind for me is techniques used to compare observed values and true values
perhasp thats a very applied math-sy viewpoint
Yea wait
(well, a righteous applied mathematician would reject the notion of "true values" in the first place)
(and use "predicted values" instead)
Srry its on Arabic
we... don't understand it
But Written: A note or observe is the first, followed by a question
Yes, I was translating
BTW What do ya think is the correct order as the last question?
what's a cool calculus fact
Is there a particular problem that sparked this comment?
well its more of how my class is set up. First of all its engineering probability so my professor is an engineer.
Second he assigns these random homework problems and i realized hes not even doing the solutions hes taking them from a pdf he found online
third the exams are wayyy too easy compared to the homeworks
and when people ask for help he barely clarifies
Do you know what kind of engineer?
electrical engineer
yea
Damm, they really are understaffed, huh.
Also like my class moves way too fast compared to the actual math major probability
like you do all the normal pdf/cdf stuff but then they just start going crazy with all this linear algebra stuff using spectral theorem
and linear algebra isnt even a prerequisite
and then thats just a load of crap for a single unit
and the final chapter is a bunch of signal processing stuff
its just so much so fast and my friends who are math majors are getting to take things slow and actually learn stuff
and on top of all of that, midterm 1 is 45% of the grade, final is 45% and homework is 10%...... and exams are take home
so basically everyone is going to just cheat with their friends
the entire class feels like a joke and i feel so unconfident in my probability skills
Normally I would talk about the borwein integrals but 3blue1brown really took the steam out of those
Made a video about borwein integrals
I don't think I watched that
tell me about it ryc!
@deep mango @deep mango @deep mango @deep mango @deep mango @deep mango @deep mango @deep mango
unless you don't want to
...why are you being nice? dont break character...
The integral of sin(x)/x on the whole real line is pi/2, this is the dirichlet integral
Oh 
fuck you
and your dog
The integral of sin(x)/x * sin(3x)/(3x) is also magically the same thing
oh right I remember this now
oh right i saw that video
As is the integral of the product when you take the first 3 odd numbers, etc. Except when you get to 15
ryc ur slow
Then it's extremely close but slightly lower than pi/2
This happens because 1/3 + 1/5 + ... + 1/13 is below 1, but when you add 1/15 it goes above 1
uhhhhhhhh
But if you use the fourier transform, you can see it
pain
The integral of a function is equal to its fourier transform evaluated at 0
oh shit rly
The fourier transform of sin(x)/x is a step function, which is 1 in between -pi/2 and pi/2 and 0 elsewhere
makes sense
Yeah. When you plug in 0, you get e^(ix0)f(x) under the integral which is just f(x).
This is harder to show, you need the fourier inversion formula for it (it's easy to show that the fourier transform of a step function is sin(x)/x, you can do the integral directly. but to go in reverse the integral is hard, so it's easier to just use the known fact that the inverse of the fourier transform just flips x to -x)
doesn't the FT make everything look more steppy
Showing the fourier transform of the step is sin(x)/x is a good exercise
Not really. Maybe fourier series?
So the idea is that a product of functions is converted to a convolution of their fourier transforms. And we know how convolutions of step functions work, or at least, we know when they're 0 and when they're 1.
I see
It turns out that the product of sin(x)/x with horizontal scalings turns into a convolution of step functions with horizontal scalings
horizontal scaling meaning scaling along the x-axis right
And you can add up the horizontal scalings to see when the convolution goes below 1 at the center of the step functions, x = 0
Yes, like plugging in 5x
ok
I see
this is p cool
Explaining how we see that the convolution goes below 1 when the scalings add up to > 1 is kinda hard tho
understandable
It has to do with the idea that convolution smudges one function by another, so we only get the biggest step function smudged down at 0 if all the smaller ones can reach from the edges (where they start smudging) all the way back to 0
The 3b1b video does a visualization of this which makes it much clearer
gmod where your very active
Sure
I think it's a really cool fact
And i was surprised to see that it actually had useful interesting math behind it
Instead of being some stupid contour integral
lol
and important for other homework problems too
Gmod did you learn laplace transforms
does the video also explain $$\int_{-\infty}^\infty \frac{\sin(x)}{x}dx = \int_{-\infty}^\infty \frac{\sin^2(x)}{x^2}dx$$
mOwOsity
it does not but that's cool
i think ive seen it
ofc
you can use fooyay
again
yes
Ok did i tell u about the inverse laplace transform yet
oh god
do I want to know
oh wait
that's just the F(s) function right
wait no nvm
ordinarily you use the table to go from F(s) to f(t) right
yeah
ok now what if i told you
based on metals history i think hes gonna go bromwich
That there was an actual formula for this
so run
makes sense
Do u know any contour integration
some
wouldn't you deal with them like line integrals
with parameterization n shit
$f(t) = \lim_{\beta \to \infty}\frac{1}{2\pi i}\int_{\gamma - i\beta}^{\gamma + i\beta}e^{zt}F(z)\dd{z}$
cofe cube (bad kernel)
This is the laplace inversion integral
yes
its related u use cauchy residue theorem
yes I'm so smart
We use the Bromwich contour
it is a mirrored D shaped contour
essentially
i will give a talk in the spring
that's fun
it is fun
Hello
metal i gave u a laplace problem but u never answered
damn
its a nice example of the residue theorem that isn't annoying
ghosted
u can finish it and include it in ur talk
thats righjt i need to do it lmfoa its saved on my camera roll
Yes
thats a rly good idea rokabe
i will do that
find the inverse laplace transform by residues
$$F(s)=\frac1{s\cosh\sqrt s}$$
hint: $F$ has countably many poles, so expect an infinite series
Because its an example of one i can't do with a table
Rocket Cube
One of my examples is one that i can do with a table
I'm scared of what your camera roll looks like
My camera roll is mostly pictures of chalkboards /whiteboards and pics of me and my gf
Or screenshots of discord
you have a gf?????
yes
no longer a math major
she was in ur micro class actually
same prof
theres another problem where u can use a table to confirm ur answer from bromwich
I'm dumb
or basically just take any table problem and force em to do bromwich instead and make sure u get the same thing
for $a>0$, find the inverse laplace transform of
$$F(s)=\frac{2a^3}{(s^2+a^2)^2}$$
to check your answer, find it again by using a table of common transforms
bois channel??
Rocket Cube
is in a different server
o
i was debating whether or not to do a slides talk or a chalk talk for this
but i think i want to keep it slides since i already have slides for it
ill just update it with some stuff because i remember i handwaved a few things awkwardly and now i feel confident enough to handwave it and say "ask me after"
same quality of lecture, just better at hiding it!
Yes exactly
I won't ask you after
yeah do slides so that u can more easily present these problems. also going thru what i posted, u should include application to PDEs
eg heat eqn with nice boundary/initial condition
solve by laplace transforms
$$u_t=u_{xx},~0<x<\pi,~t>0$$
with boundary and initial conditions
$$u_x|{x=0,\pi}=0,~u|{t=0}=x^2$$
Rocket Cube
ugly
this is one of the nicest pde
still ugly
the gist is u can transform each side of the DE
$$\L(u_t)=\L(u_{xx})$$
and say $U(x,s)=\L(u(x,t))$, so that
$$sU-u|{t=0}=U{xx}$$
Rocket Cube
ahh
this gives
$$U_{xx}-sU=-x^2$$
then transforming the boundary conditions gives boundary conditions for $U$
$$U_x|_{x=0,\pi}=0$$
now solve this in $x$, its straightforward
Rocket Cube
then the tedious part is the inverse transform 
@exotic vigil that's rough
what?
Please don't let people's expectations of you determine your actions
It's only a recipe for misery
yes i dont really care thats why ive been able to do extra studying
they are usually my own expectations like not doing something that i can
How much time do you spend on math on average btw
i used to be doing 2-3 hrs/ day now ive reduced that

6-8

ill inform my advisor of that
hello dark cube
Time to do a PhD in discord math
uh, im here all the time at least
lmao
Lmao
hrrnngg im trying to defend my catboy dissertation but my discord kittens won't let me prepare in peace

uwu
If you were writing something, and you had to talk about the following sets:
- { f | f: A → B }
- { x : |x| < f(x) }
Would you stick with colon or bar, or just use both?
I would stick with my bar macro
{ x | |x| < f(x) }
still alright for me
{ f : f: A → B }
I do like { f | f: A → B } a bit more compared to B^A
But yeah bar aint so bad: { x | |x| < f(x) }
I use colon if there's a bar next to it (like absolute value)
Nothing wrong with that
but bar otherwise
Bar with lots of absolute values and divisibility can get kinda goofy
But if this was in a single document, would it be weird/wrong to use multiple styles?
I mean I feel like there should be nothing wrong with using multiple styles depending on whichever is suitable for the situation.
You can always just explain things in words if it gets confusing.
I'd just say, "Whenever it's clear, I'm gonna use : or | for sets k?"
Like I feel it's rather silly to say "style must be consistent", compared to, "whatever is most readable"
So while I value consistency
I value readability just a little more
so I will be consistent unless it hampers readability
Weird? sure
But right now the stuff I write the most (homework) will be read by others
so I optimize for readability
Yea I agree with that
Though
you could argue that I should use colon for everything then
and to that I say "old habits die hard"
Generally, I agree with that, too, but in this specific case with set builder notation, I don't think there is an example that is super unreadable.
:
I use bar
Spamakin🎷

so many bars
a bit of spacing might help
yea true
@neat frost would love this
anyways, why would you use subset in set builder
but then the issue is not really in the set builder bar, but in ||S| imo
thats just silly
a set of sets?
but it's not a power set
OH nvm
yea I guess
but still I wanted to just cram as many bars as possible
,,{S\in P(\bZ_{100}):2\mid\abs{S}}
yea
Yeah there's always something you can do to make the situation better:
Maybe like 2 | card(S)?
this is a case where I would just say write divides
Yeah same probably
no matter how you dice it, divides next to a cardinality is weird
,,{S\in P(\bZ_{100}):(\exists n\in\bZ)(\abs{S} = 2n)}
actually this is something I struggle with teaching students at the beginning of the discrete math class I TA
No.
A good number of them get in their heads that like "yes this is rigourous math. I must use words" and I get symbol vomit
$${S\in P(\bZ_{100}),|,\exists n\in\bZ\colon\abs{S} = 2n}$$
I'd probably do { S∈ P(ℤ₁₀₀) : ∃ n∈ ℤ(|S| = 2n) }
I'd just write divides or the word even
i dont like using : after there exists
zan cube
it just doesnt make syntactical sense when the same isnt done for forall
I think a programmer's mindset is missing from a lot of symbol grammar
Which can make the symbols become ambiguous
From a programmer mindset, the lack of standard is uncomfortable
But yeah, I like to imagine colon and exists is fine since, and just stick with no colon.
Though lack of standard means flexibility in thought I'd like to think. But who knows.
im more annoyed by ambiguity - order of operations doesn't seem to be standardized or made clear I think?
,,\forall x P(x) \implies Q
for stuff like this, as an example
and i think thats partially because we discourage this notation anyways until you get to logic
But its like you introduce these symbols, discourage them from being used in proofs, and end up with something wishy washy
Yeah, I mean in logic we define it all more precisely, where as in math it's generally wishy washy and as long as it makes sense.
I think the main idea though, is that we shouldn't get so caught up in the syntax as that's not what we're studying.
But the ambiguity can be discomforting sometimes.
I agree - the meaning is important. And I've seen a lot of places where I would've appreciated a short symbolic statement rather than 3 lines of words which mean exactly the same
And I've seen a lot of notes where by mistake there can be 2 meanings due to lack of brackets in words
Just a bit curious, what prereqs are normally required for abstract algebra?
comfort with writing and understanding proofs
Sometimes linear algebra is nice to have but like
for the first pass thru group theory it might not show up so it wouldnt be needed
but there are a number of examples involving linear algebra
eventually it will be required
I see. Tysm!
dual spaces
interesting
any decomposition
And transpose
spectral theorem
included in any decomposition
for some reason my brain only associated things like LU, cholesky, and QR to decompositions lol 
i think rank nullity is a very cool basic linear algebra concept
goddamn everyone's pitching in lmao
and dual spaces aren't that uninteresting
um of course this is in the standard curriculum but lmao
lol
why is a dual space called that
what's so dual about it
the definition doesn't make it sound dual-y
This is not a concept but any norm preserving operator on R^n is linear
idfk
you have the perspective of functions acting on elements
You swap the roles of linear transforms and vectors
ohhhhhhh
but there's a dual perspective where the functions are the elements, and the elements are the functions
ok that makes sense
you evaluate an element at a function by doing function(element)
yeah
the duality comes through an identification of a vector space with its dual space through choice of an inner product
it's the same thing but you view elements as being functions on the set of functions
because the bidual is not always the original space (?)
idk if i'd agree with that being where the duality comes from
BIDUAL????
This is a certified non FDVS moment
dual space of a dual space
pain
but choice of inner product induces a natural isomorphism from V to V*
how do you think about it?
What they mean is
so every element in the vector space gives you an element of the double dual space (V*)*. an element of the dual is a linear functional to the base field (say, R), so and element of the double dual is a linear functional from (linear functionals) to R
Think of $f_a(x)= \langle x,a \rangle$
Drake
it induces a pairing and flips arrows. i don't think about dual vectors identified with vectors pretty much ever, even in the presence of an inner product, unless there is really convenient reason to do so
to me this gets too confusing
like
i'd rather keep track of what's a bra and what's a ket because they transform differently
You do physics?
covariant and contravariant vectors 
in particular, one linear functional on the space of linear functionals is given by a vector v in V. it just takes a linear functional f and returns f(v).
this is called the "evaluation functional"
oh I see
in a finite dimensional space, it turns out that EVERY element of V** is an evaluation functional
and that V** is actually just V again
but in infinite dimensions this fails
i imagine concretely like if i have a linear transformation V : R^3 -> R^2 then with the standard inner product i can identify R^3* and R^2* with R^3 and R^2 repsectively, and then think of V* as a map from R^2 -> R^3 kinda like the inverse
and somehow it feels like the spectral theorem tells you this is a good way to imagine things (in the sense that it gives a clear geometric intuition for the transpose)
in infinite dimensions, it still holds for so-called reflexive Banach spaces
e.g. every Hilbert space by Riesz rep theorem
Now listen up, fuckers
kinda like
have a great one
gn chmonkeee
gn!
gn
Have a good night chocobee
goodnight chmonkey
riesz rep
i wonder if i can give a talk to math club about it
hmm
how to speedrun dual spaces
yes
Does anyone know multiplicative inverse
Sounds advanced
Jesus loves yall
I don't like Jesus
He's not my type
Man needs a shave
I'm going live now on twitch.tv/goofthegoof where I'm working through every question of dummit and foote. come say hi if you're interested.
please do not advertise your twitch channel here
also for the sake of your sanity dont do every question in D and F
serenity what is 5w4 
enneagram type

i swear im not an hsct
dont know if you should be proud of that.

so this is what 5w4 means
wdym by hsct?
high school cat theorist
yup
runs away
Ugh infps
Turn to Him bruh He can save u
He aint even look like them pictures 🦦
How do you know?
Save me from what? I'm pretty safe I'd think
cuz He aint white
people think that but in reality (im saying this in a loving way) we all want you to go into heaven instead of hell
ye but still those were made by some random guy like 10 years ago
i'm an infp, so i'm not a math person 
I'm sure god wouldn't let such a petty thing as not worshipping him stop me from going to heaven 🙏
if you dont worship God or follow God who else would you be serving completely?
the devil
Why? I don't serve the devil
if you dont serve God who else is there to serve?
God is good and created good so therefore by doing evil wouldnt you be serving evil?
Who said I'm doing evil?
without faith it is impossible to please God
without following God there is no middle area you either serve Him or the devil
That sounds pretty petty
I wouldn't get pissed at someone just because they weren't constantly worshipping me
How come?
He doesnt hate people who try to follow Him
cuz if you arent doing good there is no neutral
There is other good than worshipping god?
He loved the world so much that He came down in human form and died for us
honoring and glorifying and exalting and praising Him can be shown by works (faith will bring works) and we as Christians still screw up daily
Does it really count as suffering if he's immortal? It's much more of a sacrifice for us to die without the absolute of immortality than for god to die with the knowledge that he is
how do i find what type i am
coz resonate with a lot of this stuff
like all the weaknesses 
He came in a human body, feeling and sympathizing with our weakness and temptations (He still never sinned), and on the cross He felt a lot of pain
He rose from the dead cuz His Spirit is immortal cuz He's God of course but in the body He could feel everything
I'm sure it's very easy to not sin if you're god, even if you are in mortal form
The tricky thing about trying to reason about this situation is establishing which part of you is God and which part of you is mortal. Mind of God in a mortal body? etc
This is blatant pushing of LEM
He came in a complete 100% human form, hence why there is the 100% God 100% man doctrine
My understanding is that basically every attempt to explain the trinity in a way that makes sense to us has been ruled some sort of heresy
ive never heard of lem what is it
law of excluded middle
3 Persons one God which work together in harmony
ohh
And the correct answer is basically that this shtick is pretty much beyond human understanding. If you accept the Christian faith (for whatever other reason you do) you pretty much take the trinity as a thing
And obv if you don't then you think it's nonsensical and its apparent inconsistency is an actual inconsistency
well ye theres only good and evil, if you dont do good you do evil, and (Hebrews 11:6) without faith you cant please Him
there literally is no middle
i dont want to please him
as a matter of fact
the country im from
there are 33 million gods
try pleasing all of them 
I don't think debating religions is really gonna get anywhere here lol
yea lol
lets debate something else
for example, why i am the best mathematician to ever live.
32,999,999 of them statues that dont have senses and arent God
Hablan español?
ye ight
Religious discussion is fine and honestly I often find them interesting
excuse me?
i agree it doesnt get anywhere\
the fuck do you mean by that
i mean theres 1 God
there isnt
why are you mad?
But the issue is that unless you're learned scholars in a religion and can debate it properly
It basically becomes a bunch of no u
EXACTLY
coz i dont like blatantly wrong bs
And it has a lot of potential to get offensive
its not wrong
im not even religious but im not gonna let you shit on something you dont know anything about
Because, let's take Christianity vs Buddhism
ye if someone even hears one thing they can freak out
i know a lot about it
I mean really just take religion X vs religion Y that are inconsistent
As far as religion X is concerned
anyone can take a piece of wood and carve it into a statue and say "god"
that is my point
People who study religion Y are just talking shit
And their whole life is misguided
thats not how hindu gods work
Very heavy accusation to levy at someone
statues are a representation of the god you are worshipping
e.g. what's happening literally right now
but when Jesus comes down to earth dies for us raises and says "I am God" that rlly means a lot
can someone help me with basic trigo
they arent gods themselves by any means
ye i would like to use verses but mostly it doesnt work, they dont have faith therefore they dont care to listen or believe, and also when I stop using verses they say "oh so you cant defend it" its rlly so hard to finish even talking about it
cuz no matter what i say ppl would get mad
nah I do not need help with sums
You can't use verses to defend Christianity because the validity of those verses presuppose the truth of Christianity
There are ways to debate religion correctly
You simply don't know how to do it
they dont believe so they will come up with anything
you believe, so you will come up with anything
you cant debate it to make them believe
why do you assume the religion you were made to believe in since birth is the correct one
Caleb I'm gonna put it to you straight, the problem here isn't them it's you lol
u think i believed it since birth?
I am not Christian and I'm fairly certain that I could defend Christianity much more effectively than you can
technically not since birth but you get my point
I believe hinduism
i wasnt taught it, i had it hidden from me in every form until someone came up to me and i get mocked even by my parents for it
I don't mean this as a flex but the problem is you can't start with saying "Oh well first if you believe the Bible than Christianity is true", you have to convince people that the Bible is what's correct
you literally cant cuz i cant do some miracles through the screen
you can try to put up a good argument
Do you know what it means to believe in Hinduism
So then don't bother caleb
i can tell u about some but yall prolly wont believe them
vishnu
thats what im saying i dont want to but if i stop they say "oh so you dont know anything"
If your defense of Christianity relies on miracles that you personally witnessed, the issue is as you say, you cannot communicate them
meditation chanting normal aarti
Ok,ig you know what you are doing
i literally came in here saying only "Jesus loves yall" and "turn to Him so you can be saved"
wbu
never intended an argument
the first part isnt offensive to say
Yeah it should've been clear to you that this would lead to a debate, or at best being ignored by anyone who didn't care
ye but i cant just leave parts out of the truth
Because "turn to Him so you can be saved" addresses people that already don't believe in Christianity
He says He's the Way the Truth the Life
Well what if you knew nothing about Jesus except "magic man who came back to life"
bro whom do I need to be saved from?


