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12:00 AM
Yeah your proof seems fine then
 
Sweet! Thanks!
 
what is the difference between writing a function sA(d) vs. s(A,D)?
 
12:19 AM
Is it safe to use a reference from nlab in a research pseudo-monograph text? Not publishing to anywhere professional of course
At least not yet
 
12:57 AM
hmm it's always interesting to visit the permalinks of the starred chat lines
 
it's always interesting to click on a user profile and see a user named "The Testosterone Fanatic"
truly a unique experience
 
1:12 AM
I take that as a compliment
 
can anyone help me figure out whether stars and bars theorem will change of Zero is not included in the sum of 10 odd integers for example ? the exact problem is " how many ways can 2018 be expressed the sum of 10 odd positive integers
 
Finally I am at the right site
I went to some weird meta.chat version and I was like where are you guys?
Anyway could I use the definition of an open set in a normed vector space?
 
doesnt this mean that no 'bars' can go on the ends and that no two bars can go in between
 
@usukidoll no you can't, it's illegal
6
 
Crud
What is the definition of an open set for a normed vector space? Metric spaces use D(x,epsilon) but I'm not in a metric space
The question I have is
 
1:25 AM
@usukidoll you are in a metric space
you live in $\mathbb{R}^3$ and that is a metric space
 
If A is open prove that A+B is open and without the open definition of a normed vector space I'm screwed unless I can also use the open set definition from a metric space djkabegwjbdns
I know triangle inequality is in normed and metric space
 
@RandinD: isn't it the same as partitioning 2008 into 10 even integers, so partitioning 1004 into 10 integers?
 
@usukidoll if $\| - \|$ is a norm, then you can define a metric via $d(x,y) = \| x - y \|$. This metric generated the topology
 
a norm is a stronger form of metric - it is a metric that also has relationships with the vector space operations of the space
 
Right but to prove that A+B I have to use the open set definition, but I'm in a normed vector space so I was wondering if I can use the open set definition from the metric space in the normed vector space
 
1:29 AM
Yes, it is the same definition, an open set is a union of open balls
 
Alrighty :)
 
1:54 AM
@Hurkyl
 
there's no such user here
 
@usukidoll You realize Daminark was joking, right?
 
Yeah
 
is anyone here excited for the next Dragon Ball Super episode airing next Saturday?
Goku's new form will be perfected in that episode
 
animu boi here
 
who the hell watches Dragon Ball Suffix-here in 2018???
 
what a pleb
only plebians watch dragon ball
real people watch naruto
 
@BalarkaSen sir i ask algebra doubt in other chat
 
lmaooo I saw that coming
 
2:12 AM
@0celo7 send bobs if you want help
 
@BalarkaSen check discord
 
dear god what the fuck
 
?
how is that bad
believe me, what I originally put was bad
@BalarkaSen so can u resolve the doubt now
 
wrote something
 
wait, there's a discord linked with this chat?
 
2:22 AM
@TheTestosteroneFanatic Balarka and I have one where we send each other naked pictures
2
 
It's true
can confirm
 
Bob
is math stack exchange a good place to post practical statistics questions?
 
it might be better suited for stats.stackexchange.com
 
@0celo7 also you meant nakde pics not naked pictures
 
Bob
thanks
 
2:28 AM
@BalarkaSen bobs, vegana, bols, beniz
 
a wonderful compilation of words from my countrymen
truly a marvel of the world
 
@BalarkaSen From the Upanishads to FB DMs
Indian literature brings a tear to the eye
 
100% truth
 
2:59 AM
@0celo7 tmi
 
@BalarkaSen
https://pics.me.me/okay-gang-lets-see-who13-year-old-trisha-really-is-28645850.png
 
haaaaaaaaaaa
 
i dont know this reference
my meme brain is failing on this one
 
this is the entire story:
https://pics.me.me/310-sanjayy-kapoor-182-likes-sanjayy-kapoor-going-on-plane-28609107.png
 
india is the greatest country
 
3:04 AM
wait, that's a poor resolution
 
LMAO
what a massive legend
my sides
 
personally, this is my favorite:
http://www.storypick.com/wp-content/uploads/2017/10/Durgesh-meme-2.jpg
 
this guy is a certified m a s s i v e l e g e n d
@0celo7 ikr? dare i say it's greater than Soviet Russia
USSR is probably my 2nd favorite country
 
1950s Iran ftw
 
@BalarkaSen let me send you to a Gulag I got for you then, son
 
3:09 AM
@TheTestosteroneFanatic He's a Gulag warden...
 
I'll write a Gulag archipelago and get that Nobel prize
get all the NSA fundings boiiii
 
@BalarkaSen I wish I had been a topologist
this fucking calculation is going to kill me
 
speaking of which, I noticed that a topology course is very rarely offered in my current uni
dunno if this is just my uni's thing or if it's a trend across all American uni's
 
no algebraic topology you mean?
 
not even a basic topology course
I mean it IS offered, just rarely
 
3:13 AM
that's...not right
 
ikr
thankfully it's not my area
 
@TheTestosteroneFanatic everyone needs basic topology
Is it even possible to do interesting mathematics without topology?
 
I did it already in my previous uni back in India as an undergrad
thankfully
 
oh
 
@The topology is often taught just at the grad level in the U.S. except at particularly large schools. The basics of topology for metric spaces are taught in real analysis. Point-set topology in general is declining as a field, and algebraic is usually viewed as too advanced for undergrads who might not even have analysis.
 
3:20 AM
@CarlMummert yeah I was taught analysis the previous semester, I saw that
however my uni is quite a large school, though not Ivy, and there's still a rare chance of me being taught topology in spite of being in my PhD
 
If there is a PhD research group in topology, they will usually have some grad courses in it to help get their PhD students up to speed. If there is no research group in topology, then it may not be as useful for them to teach
 
I see
that actually makes sense. My current uni was recommended to me by my prof because of my interest in probability
 
I feel like some point set topology is essential for doing algebraic topology and doesn't really belong to the algebraic topology course syllabi
But it's weird because it can also be picked up while learning
 
Algebraic topology doesn't require a lot of the material from point set topology - just the basics and a few lemmas which may not even be covered in a dedicated point set class (like the Lebesgue number lemma)
A dedicated point set class is more likely to look at complicated separation properties, metrizability, fancy kinds of bases, etc. - which are not very interesting when every space you look at it already a metric space and often a compact metric space, which is the case in algebraic topology
 
Well not unless you really want to figure out the topological foundations of CW complexes
Which is important but also appendix material in most algebraic topology texts
So I suppose you're right in a sense
I'm probably a bit biased because I have been thinking too much about various function spaces lately. :P
 
3:35 AM
@CarlMummert how can you NOT cover Lebesuge number lemma in a point set class
 
@0celo7 the T 3 and a three fourth spaces are more important
a topological group which is T1 is T3
the greatest theorem of all time
 
Sure, it's a great result, but content depends on what you want to achieve. You don't need that lemma to do the basics of separation, compactness, connectedness, or metrizability for general spaces. It gets used in analysis and algebraic topology, but for example in the kind of point set topology I have worked on we would never need it.
 
Point-set topology is a great source of counterexamples nevertheless
Even in algebraic topology. It justifies a lot of niceness assumptions
Which is not essential, but still motivating.
 
Lebesgue is such a good lemma
Top 5 Theorems: Lebesgue Number Lemma, Gromov-Lawson, Hodge Decomposition, Choquet-Bruhat-Geroch, 2+2=4-1=3
 
tfw when you don't have a 5th candidate so you quickmaffs
 
3:46 AM
@BalarkaSen skrra pop pop
 
rrratnum skrrrutnum
 
@BalarkaSen actual number 5 is the snake lemma
 
No love for Pythagoras
 
The whole business with the compact-open topology is point-set as well
and that's really important in homotopy theory
 
So, my top 5 would probably be mostly analytical because that's the subject where I know interesting theorems and know their proofs completely
I love Dold-Thom and all but I don't know the proof that the E-S axioms define stuff uniquely
 
3:55 AM
I don't know the proof of Gromov-Lawson
I think I'll take a crack at it though
 
So, I am TAing a course with 130 students; they have an exam tomorrow; I held a review session today in order to help them prepare for the exam. The review session was held online, which means that they didn't even have to come to campus. Of the 130 students, a grand total of maybe 15 or 20 showed up.
 
All spaces are locally compact, sane, all that jazz. The only reason people care about counterexamples in point-set topology is so they know what properties they need to put into their proofs.
 
My actual list would be different
 
There are going to be a large number of students that are going to have to take precalculus again next quarter, methinks.
 
@AkivaWeinberger "All spaces are locally compact"
Think about that a bit
 
3:56 AM
Like, otherwise you might keep on trying and failing to prove a theorem because you never took advantage of its Hausdorffness or something
 
L^p isn't a space tho
 
@0celo7
 
@0celo7 Oh I guess I excluded $\Bbb Q$
 
????????????
 
you should see 1950 Alexandria
 
3:57 AM
Whatever, who cares about the topology of $\Bbb Q$ anyway
 
Ever heard of Banach spaces
 
Yo mama so fat, she ain't locally compact!
 
Isn't L^p a Banach space
 
Only vaguely tbh @0celo7
 
yeah it is @BalarkaSen
 
3:57 AM
@AkivaWeinberger The only locally compact topological vector space is $\Bbb R^n$
 
Only the French use the vague topology; here in 'Merika, we call it the weak-$\ast$ topology.
 
Anyone recommends a movie ?
 
non locally compact spaces are actually important but in analytic contexts
 
@Adeek Apollo 13
The Social Network
 
3:58 AM
oh I never watch Apollo 13
I will try it
 
Both easily pirated within minutes
 
Gah my notes from 4 months ago are awful
I have number = number + polynomial wat
 
@0celo7 I am originally from Alexandria in 50s it was amazing
but now it is shuuuut
 
@Adeek ur not that old
 
@Adeek to answer your question, yeah someone recommends a movie
 
3:59 AM
@0celo7 I am not lol
I mean from the pictures
 
Also, education back then was nice
now it is also vvery bad
 
~$wikilookup Pre-Code_Hollywood
 
4:00 AM
"I am originally from Alexandria; in the 50s, it was amazing."
 
Pre-Code Hollywood refers to the brief era in the American film industry between the widespread adoption of sound in pictures in 1929 and the enforcement of the Motion Picture Production Code censorship guidelines, popularly known as the "Hays Code", in mid-1934. Although the Code was adopted in 1930, oversight was poor and it did not become rigorously enforced until July 1, 1934, with the establishment of the Production Code Administration (PCA). Before that date, movie content was restricted more by local laws, negotiations between the Studio Relations Committee (SRC) and the major studios, and...
 
Pick your favorite movie
 
@AkivaWeinberger you know what I mean :P
 
OK how do I make something bold
Test ;
OK why was that not working
 
@Adeek use commas bro
 
4:03 AM
yeah I should do that @0celo7 :D
 
@0celo7 No,
 
@0celo7 what is a "commas bro"?
 
@BalarkaSen momma told me not to sell work
 
Carl M if you are still on here --the chat room yes it is
since thier are 1004 odd numbers up to 2018
 
1009, no?
 
4:05 AM
wot
 
what im trying to figure out is if the wording is not right on the probel i was given on an exam and told professor he was wrong
well yes akiva 1009, but if u use the 'minimum ' of 9 1's
and one 2009 then number of odds less then 2009 are 1004
whats wired is he said " positive integers" and that would mean NO ZEROS
right?
the exact problem is " how many ways can 2018 be expressed the sum of 10 odd positive integers
using stars and bars on this would include zeros would it not?
 
hey @0celo7 do you want to have good complex analysis problem ?
 
If you do it right you can get it not to include zeroes
 
no thanks
 
ho akiva??
 
4:10 AM
@AkivaWeinberger complex analysis ?
 
how
 
@BalarkaSen @MatheinBoulomenos do you guys want complex analysis problem ?
 
Like I guess you have * _ * _ * _ * _ * _ * _ * for example if you want to express [counts] seven as a sum of stuffs
 
how can u ensure two bars dont go among the n+k-1 spaces ? :(
 
4:11 AM
I am gonna mention it anyway :P as a challenge problem
 
or that bar(s) dont on eaither 'end' of the string of stars?
 
We don't want two bars to go in the same place, 'cause that'd be a zero
 
Suppose that f is entire. Suppose that $f(z) = f(z + \tau_1) = f(z + \tau_2)$ such that $\tau_1,\tau_2$ are L.I over $\mathbb{Q}$, then show f is constant.
 
and we don't want bars on either end 'cause that would be a zero also
 
no sh%T thats why i dont thinbk stars and bars will work on this
UNLESS the wording says "positive integers"
 
4:12 AM
there is really easy way to solve this and a really hard way to do it
 
I still have no idea what stars and bars are
 
stars and bars Ocelo ? hold on let me send u link to wkipdeia
 
@RandinD But if you do want positive integers, you just need to ensure those to things and it's not that hard
 
oh no
I don't want to know
 
In the context of combinatorial mathematics, stars and bars is a graphical aid for deriving certain combinatorial theorems. It was popularized by William Feller in his classic book on probability. It can be used to solve many simple counting problems, such as how many ways there are to put n indistinguishable balls into k distinguishable bins. == Statements of theorems == The stars and bars method is often introduced specifically to prove the following two theorems of elementary combinatorics. === Theorem one === For any pair of positive integers n and k, the number of k-tuples of posi...
why not ? u are on here to learn math arnt u??
 
4:13 AM
stars and bars is combinatorics, not math
 
@RandinD Look at Theorem One and Theorem Two on that page
 
@AkivaWeinberger I'm trying to break this bot. Join me in Sandbox
 
@BalarkaSen sanity check, $F=0$ to first order means $F(0)=DF(0)=0$, right
 
Yep
 
Stalin keeps calling that second order
I don't know what she's on
 
4:15 AM
so i was right its (n-1)C(k-1) NOT (n+k-1)C(k-1) ?
 
Akiva ..u still there?
that will not include zeros as in *******|*||
*******||*|
******|**||
**|**|**|**
*****|*||** INCLUDES ZEROS in the sum which is a NO-NO when you want the sum of only postive intgers
 
@Adeek I have always suspected that I have very little empathy. I always have to enforce it on myself and actively picture myself in others' scenarios in conversations to be empathetic
 
I don't have time for empathy while studying the way of the blade
 
ooo... edgy
(see the pun?)
 
4:27 AM
no, can you point it out to me?
 
@The "I always have to enforce it on myself and actively picture myself in others' scenarios in conversations to be empathetic" That's exactly how every person in the whole galaxy understands morality
Non-biological morality at least
Do you want to get your ass beaten for no reason when you're talking to someone? No
Then you prolly shouldn't kick someone's ass randomly
Simple logic
 
that's why I preemptively beat people's asses before talking to them
 
unchristian masochist
 
how dare you
 
@BalarkaSen I mean, it's a little more complicated than that. When someone is talking with me, I have a hard time paying attention to them. But I force myself to exactly picture their feelings and what they would be going through whenever they're describing a past experience, eg
 
4:32 AM
@TheTestosteroneFanatic For me I am quite the opposite.
 
@TheTestosteroneFanatic I feel bad whenever someone is in pain. I always try to help people in need.
@TheTestosteroneFanatic the other day there was some homeless guy in the street. He asked me to give him some money to buy food. Even though, I knew he would probably buy drugs with it. I gave him 20 dollars
 
lol
 
wow 20 dollars is a lot
 
yeah I felt super bad for him.
 
4:34 AM
that guy had some nice meth thanks to you
 
I am still a student too I don't make a lot of money.
yeah that is something I need to fix in myself
 
just tell yourself that you need to be helpful just like you are, but you also need to be more discriminating about who you decide to help
as in, help those you think that deserve it more
 
yeah
 
donate to the clinton foundation
 
@TheTestosteroneFanatic Do you like forcing yourself to do that?
 
4:37 AM
I have to force myself the other way
basically, I'm an asshole trying to be nicer than I would naturally be (I think)
 
I'm asking why you try to do that
The reason should boil down to "to not get my ass beaten"
 
@BalarkaSen are you actually worried about physical encounters?
 
@0celo7 no but you should be
 
why?
 
folds sleeves
 
4:40 AM
@TheTestosteroneFanatic Altough, I like being alone more than surrounding myself with friends
 
I have a Wakizashi on me at all times
 
realizes he's wearing a t-shirt
@0celo7 I thought you Americans had guns with you not swords
What happened?
 
@Adeek for me, again it's the opposite. I like having friends, but because of being in university, it's really hard for me
 
A sudden shift to more primitive weapons I see
 
@BalarkaSen commies said no guns in school
 
4:41 AM
lmao
 
Wakizashi counts as a religious device
so it's A-OK
 
@BalarkaSen I am worried about prison, so yes in a way I'm worried about physical encounters (they will be much more than just 'encounters' especially if you drop the soap)
 
loooooooool
 
lmao
 
math chat GONE SEXUAAAAAAAAAL
 
4:43 AM
PRANK EDITION 679
GONE WRONG
 
@TheTestosteroneFanatic I see
 
pranks in the math chat (MUST SEE)
@BalarkaSen did you see the latest h3 vid?
 
it was a surreal meme
 
@0celo7 Oh the Prank Invasion returns vid?
It was fucking great
 
4:46 AM
would you guys like to hear nice solution to problem I posted earlier ?
 
yes adeek
 
You remember the problem ?
Since $f$ is entire we have that $f(z) = \Sigma_{n \geq 0} \frac{f^{n}(0)}{n!} z^n$
by assumption we have that $f(z) = \Sigma_{n \geq 0} \frac{f^n(0)}{n!}z^n = \Sigma_{n \geq 0} \frac{f^n(0)}{n!}(z + \tau_1)^n = \Sigma_{n \geq 0} \frac{f^n(0)}{n!}(z + \tau_2)^n $
so in particular for z = 0 we must have same equality. But that means for N big enough we have $\Sigma_{n \geq 0}^{N} \frac{f^{n}(0)}{n!} * (\tau_1^n + \tau_2^n)$ since $\tau_1$ and $\tau_2$ are linearly indepedent we must have coeffients being zero.
so we must have that f is constant.
@RandinD
 
@Adeek You mean $\tau_1^n - \tau_2^n$?
 
yeah
yeah typo
 
So you know $\sum_{n \geq 0} f^n(0)/n! \cdot (\tau_1^n - \tau_2^n) = 0$. Why does that mean you can chop off terms after some big enough $N$ and say the same thing?
That sounds suspicious
 
4:54 AM
Don't we know that in order for infinite series to converge the coeffients must be eventually go to zero. I am not sure how to make that part rigorous.
 
The terms can converge to zero without being zero.
 
doubly periodic function stuff?
 
yeah @Semiclassical
yeah
 
I believe this proof is unfixably wrong. It's not as simple to prove that doubly periodic entire functions are constant.
You need Liouville's theorem
 
I mean I do have another proof
but that other proof is like 2 pages long
 
4:56 AM
There's a 2 line proof.
 
really ?
how ?
 
Take the parallelogram with vertices $0, \tau_1, \tau_2, \tau_1 + \tau_2$. The function is bounded on that parallelogram because continuous functions on compact domains are bounded.
 
I'm running out of energy to write this thing
 
Doubly periodic means the function is translates of that function on that parallelogram along the lattice $\tau_1 \Bbb Z \oplus \tau_2 \Bbb Z$
 
please Yau, take my soul
 
4:58 AM
So it's bounded everywhere
Hence constant
 
oh
I see
nice proof
 
Of course, things become interesting again once you ask about meromorphic doubly periodic functions
then you get elliptic function theory and theta functions etc
 
In fact it means any doubly periodic meromorphic function must have infinitely many poles. Why?
 
can you tell me more about this ?
 

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