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Nick
Nick
11:00 AM
@robjohn: oh.. I get it.
lol
That'll be my reply from now on.
I don't suffer from many courses, I enjoy every one of them :D
@Huy: Well, I'm out of ideas. I'll go back to my first one. Graphs. Unless, your students can all perfectly graph out $y = \arccos(\cos x)$ in under 2 minutes, then I think teaching them the basics will be beneficial. Plus, you can throw in things like how acceleration, velocity and displacement are related to each other graphically.
 
Huy
Huy
@Nick: They can and I already did. :D
 
Nick
Nick
@Huy: Well, let me say you are very excellent teacher and I wish you had taught me.
@Huy: And they know Matrices and determinants?
 
Huy
Huy
@Nick: No, I will teach them at the beginning of 2015.
@Nick: Standard curriculum.
 
Nick
Nick
@Huy: What about series and sequences?
 
Huy
Huy
@Nick: Already seen to a certain extend and I doubt they care about them.
@Nick: I don't even care about them, so why would they. D:
 
Nick
Nick
11:10 AM
lol
@Huy: ... Well, have you covered everything in Hall & Knight: Higher Algebra
(that's a pretty famous book. You must have heard about it)
 
Huy
Huy
Never heard about it.
1984 is a famous book. I've heard about that.
 
Nick
Nick
Yeah, George Orwell. Nice book.
 
Chris's sis
Chris's sis
@robjohn something shockingly beautiful is coming ...
 
Nick
Nick
@Huy: Hall & Knight is the basic math book to have done before college. It's kind of like Irodov for Physics except compared to Irodov, Higher Algebra is a wee naked crying babee.
 
Chris's sis
Chris's sis
@robjohn
Prove that

$$\lim_{N\to\infty}\left(\sum_{n=1}^{N}\frac{H_n}{n}\sum_{k=1}^{n-1}\frac{(-1)^k}{k}+\log(2)\sum_{n=1}^{N}\frac{H_n}{n}\right)=\operatorname{Li}_3\left(\frac{1}{2}\right) $$
 
Huy
Huy
11:19 AM
@Nick: Never hard of Irodov either.
 
robjohn
robjohn
@Chris'ssis I will look at that now
 
Chris's sis
Chris's sis
@robjohn Wait, another one is coming ...
 
Nick
Nick
@Huy: ... Ok, I reccomend you get Irodov, because it's too awesome of a problem book. It's entirely physics but it's just too awesome.
 
Huy
Huy
@Nick: I've done a lot of awesome physics.
 
Chris's sis
Chris's sis
@robjohn Prove that

$$\lim_{N\to\infty}\left(\sum_{n=1}^{N}\frac{1}{n}\sum_{k=1}^{n-1}\frac{(-1)^k}{k}+\log(2)H_N\right)=\operatorname{Li}_2\left(\frac{1}{2}\right)$$
@robjohn and the whole limits family is in my hand now. :-)
 
Nick
Nick
11:22 AM
@Huy: Well, the questions are for high schoolers. So, it's not too hard but solving the entire book is something professors in my country brag about. It's almost impossible to do.
 
Huy
Huy
@Nick: Professors in my country don't really need to brag.
 
Chris's sis
Chris's sis
@robjohn I'm d**n happy now. :D
Thanks God for this achievement! :-)
 
Nick
Nick
@Huy: lol, but it's kind of like climbing Mount Everest. Do it for the same reason you'd climb that mountain.
 
Huy
Huy
@Nick: I would never want to climb that mountain. :D
 
Nick
Nick
@Chris'ssis: I have never heard of d**n
Aw gross.
remove it
@Huy: Then don't get Irodov. lol
@Huy: So, what have you decided to teach?
 
Huy
Huy
11:26 AM
@Nick: I'm doing some research about basic game theory just now.
 
Nick
Nick
@Huy: That's pretty good. It's a nice idea. Draw them in with it's applications. Then trap them in theory :D
 
Huy
Huy
@Nick: I thought of the problem about splitting a sandwich into three parts last week already and I thought it would probably sound interesting and it is very accessible. But I'd need to go learn some game theory.
@Nick: So far, it's just basic linear algebra.
 
Wildhorn
Wildhorn
Hey
@Masacroso I can't be here for long, about to get to work
 
Nick
Nick
@Huy: That'll be good for when they start matrices. But when you say basic linear algebra, do you mean vector spaces? (Sorry, I've never attended a formal class on it)
 
Huy
Huy
@Nick: I'm watching a very basic series of videos and it's just matrix multiplication so far, because it's the just the two-player zero-sum game.
 
Masacroso
Masacroso
11:37 AM
guys, hi... I need help... I cant see here mathjax code
 
Committing to a name
Committing to a name
What is a fun textbook to learn some advanced math?
 
Ice Boy
Ice Boy
@Huy why not ask them what they want to learn?
 
Huy
Huy
@IceBoy: Because it is a course offered to all pupils of that age and I only have very few of them as my pupils.
 
Ice Boy
Ice Boy
@Huy do they give you a list of topics?
 
Huy
Huy
@IceBoy: No.
 
Committing to a name
Committing to a name
11:43 AM
I am currently doing: Rudin's Analysis, Lee's topology, Tao's measure theory and Kreyszigs Engineering text. Any other books I should be doing?
And Heinemanns Chemistry, since my Chem knowledge is terrible
 
Will Hunting
Will Hunting
@Committingtoaname This is a very random and broad question, hence unanswerable.
 
Committing to a name
Committing to a name
Hence it is in the chat section, where rigour isn't required
Any other books you guys like*
Or take it however you want, just throw some Math texts
 
Will Hunting
Will Hunting
@Committingtoaname Have a look at my 12 holy books, hang on...
 
Committing to a name
Committing to a name
Or tell me my books are terrible
 
Will Hunting
Will Hunting
2 days ago, by Will Hunting
Marsden's Calculus I, Calculus II, Calculus III; Cohn's Classic Algebra, Basic Algebra, Further Algebra; Rudin's Mathematical Analysis, Real and Complex Analysis, Functional Analysis; Lee's Topological Manifolds, Smooth Manifolds, Riemannian Manifolds.
 
Committing to a name
Committing to a name
11:47 AM
I have: "Rudin's Mathematical Analysis, Real and Complex Analysis, Functional Analysis; Lee's Topological Manifolds, Smooth Manifolds, Riemannian Manifolds."
And am working throught The first of Rudins and Lee's atm
through*
 
robjohn
robjohn
@Chris'ssis Using this answer, I get $\frac12\zeta(2)-\frac12\log(2)^2$, and using this answer, I get that $\mathrm{Li}_2\left(\frac12\right)=\frac12\zeta(2)-\frac12\log(2)^2$
 
Committing to a name
Committing to a name
@WillHunting What is expected of Marsdens Calc 3?
 
Will Hunting
Will Hunting
@Committingtoaname You can take a look at its contents page to find out more.
 
Chris's sis
Chris's sis
@robjohn Nice. Aren't these limits amazing? :-) I wonder how I missed them so far ...
 
Huy
Huy
@Committingtoaname: Do QFT in a nutshell.
 
Chris's sis
Chris's sis
11:51 AM
@robjohn ah, OK. That one can be got from reflection formula too.
 
robjohn
robjohn
@Chris'ssis do you have a more direct way to show that it is $\mathrm{Li}_2\left(\frac12\right)$?
@Chris'ssis I show the reflection formula in that answer. That is what I used.
 
Chris's sis
Chris's sis
@robjohn OK
@robjohn I have some in progress.
 
Committing to a name
Committing to a name
@WillHunting Is it meant to start from page 645?
 
Will Hunting
Will Hunting
@Committingtoaname Yes, the three volumes have one page numbering.
 
Committing to a name
Committing to a name
@WillHunting I like that
@Huy How much Math does one expect in QFT in a nutshell? Or is it solely conceptual?
i am NoT currently downloading qft in a nutshell
 
Huy
Huy
12:02 PM
@Committingtoaname: Good. I don't think you should download it. The author put a lot of effort into it and it turned out great.
 
Ice Boy
Ice Boy
How does down loading it change that?
 
Committing to a name
Committing to a name
If I couldn't possibly afford the books, wouldn't downloading them only potentially increase propagation of the book, hence it is only potentially positive?
 
Huy
Huy
@IceBoy: I don't support thieves.
 
Ice Boy
Ice Boy
:-O I'm not a thief.
When people use books from the libraries are they thieves?
Unless you are reselling them for a profit.
 
N3buchadnezzar
N3buchadnezzar
@IceBoy but they hand them back
 
Ice Boy
Ice Boy
12:13 PM
They can photocopy them.
I have
 
Committing to a name
Committing to a name
You can never steal knowledge, learning is simply too valuable
 
Ice Boy
Ice Boy
Are we trying to make a profit on someone else's work?
 
Committing to a name
Committing to a name
I profit in joy
 
Ice Boy
Ice Boy
That^ is what the author intended.
 
Committing to a name
Committing to a name
But I stole that joy
 
Huy
Huy
12:18 PM
@IceBoy: If I go to a store and steal a TV it is considered stealing, no matter whether I'll be just using it at home for personal joy or I sell it on eBay.
 
Committing to a name
Committing to a name
You stole their profit though
If I have insufficient means(money) to obtain the book regardless, I am not taking profit, but I am increasing the chance of other people buying it
 
Ice Boy
Ice Boy
Then all the libraries in the world are full of stolen material.
 
Huy
Huy
@Committingtoaname: I could say the same thing about a car. I have insufficient means (money) to obtain a BMW regardless, so I am just increasing the chance of other people buying it by stealing it?
I don't think that makes any sense.
 
Committing to a name
Committing to a name
@Huy In that case once again, you are stealing money from others
 
Chris's sis
Chris's sis
@rehband look here ...
 
Committing to a name
Committing to a name
12:21 PM
I am not however
 
Huy
Huy
@Committingtoaname: Yes, you are. You just don't realise it.
 
Committing to a name
Committing to a name
How so?
 
Huy
Huy
@Committingtoaname: If you went to a book store and bought it there, some people would profit.
 
rehband
rehband
@Chris'ssis Impressive limit, wow
 
Committing to a name
Committing to a name
But I can't afford it, in either scenario of me downloading or not, they gain no money
 
Chris's sis
Chris's sis
12:22 PM
@rehband Thanks. This what the reader finds in my book. :-)
 
Committing to a name
Committing to a name
If I don't download it, I will read it at a library, Hence no profit
 
Gustavo Montano
Gustavo Montano
I can't wait to move out.
And just do maths in my room for the rest of my life
 
Huy
Huy
@Committingtoaname: Neither can I afford an expensive car, so in either scenario of me stealing one or not, they gain no money.
 
Gustavo Montano
Gustavo Montano
I can't wait to grow old when all I need are books paper and pen
 
Committing to a name
Committing to a name
In the car situation, you are robbing something physical, creating loss, I am not
 
Ice Boy
Ice Boy
12:23 PM
@Huy it should be illegal for libraries to have photocopying machines in them, right?
 
rehband
rehband
@Chris'ssis =)
 
Chris's sis
Chris's sis
The problem with stealing stuff is that the stealing does not make you better. I know I'm on the right way and one day I'll be like Ramanujan.
 
Committing to a name
Committing to a name
In your scenario you have person A gain $10000 car, and person B lose $10000 car. In my scenario, it is option A: don't download, Person A Gain $0, Person B lose $0, in option B: I download, Person A gain $65 book, person B lose $0
 
Huy
Huy
@Committingtoaname: So if I'm hacking someone's e-banking account and transfer all his money to my account and use it with my debit card, I'm not creating any loss because the money was never physical, right?
 
Committing to a name
Committing to a name
If you would read my above post, you will find the issue, once again you have Person B losing
 
Sawarnik
Sawarnik
12:25 PM
@Huy @rehband Hi.
 
Committing to a name
Committing to a name
Where person B is simply not gaining, which he wouldn't gain regardless, since I cannot afford to buy
 
rehband
rehband
@Sawarnik Hello Sawarnik!
 
Sawarnik
Sawarnik
What is the matter? @Committing
 
Committing to a name
Committing to a name
In your scenario you have person A gain $ from bank, and person B lose $ from bank. In my scenario, it is option A: don't download, Person A Gain $0, Person B lose $0, in option B: I download, Person A gain $65 book, person B lose $0
 
Huy
Huy
@Committingtoaname: Person B loses $65 in the latter case.
 
Committing to a name
Committing to a name
12:27 PM
No he doesn't he simply doesn't gain
 
Huy
Huy
@Committingtoaname: He should gain $65 but you take it away from him, i.e. stealing.
 
rehband
rehband
@Chris'ssis Do the gods reveal these limits to you in your sleep?
 
Committing to a name
Committing to a name
But in the ONLY two options, I either download it or not. Download means nothing, don't download and I STILL cannot buy, hence he cannot gain. There is no event in which he gains
 
Ice Boy
Ice Boy
Stop calling me a thief.
 
Sawarnik
Sawarnik
@rehband Ramanujan :D
 
rehband
rehband
12:28 PM
@Sawarnik Lol exactly
 
Sawarnik
Sawarnik
Such powers!
 
Ice Boy
Ice Boy
When you take notes in class are you stealing?
 
Chris's sis
Chris's sis
@rehband There is one god amongst these ones that revels to me more limits than anyone else, and his name is Very Hard Work. :-)
 
Sawarnik
Sawarnik
@HipsterMathematician You are the cat, aren't you? :D
 
rehband
rehband
@Chris'ssis That's the best God :P
 
Chris's sis
Chris's sis
12:31 PM
@rehband Yeah, sometimes I have interesting dreams, I dream myself as a super human able of amazing things, and also see some interesting questions.
(most of the time, I forget them when I wake up)
 
Sawarnik
Sawarnik
@Chris'ssis Exactly :D
 
Chris's sis
Chris's sis
@Sawarnik unfortunately :-)
 
Committing to a name
Committing to a name
@Huy In any case, I will not download the book, since you recommended it, and it is your will against it.
 
Sawarnik
Sawarnik
@Committingtoaname What is the matter?
 
Committing to a name
Committing to a name
@Sawarnik Long story ;)
 
Sawarnik
Sawarnik
12:34 PM
@Committingtoaname Do you want to download a book?
 
Ice Boy
Ice Boy
@Huy you make some good points :-)
 
Sawarnik
Sawarnik
Then where is the problem? @Commit
 
Ice Boy
Ice Boy
The problem is he is not committing to a name :-)
 
Committing to a name
Committing to a name
@Sawarnik It was a moral problem, not a math problem haha. It started with a book recommendation, and then arguing over whether downloading when you don't have funding to buy in the first place is theft. It is done now
 
Sawarnik
Sawarnik
@Committingtoaname Hmm. Can I put my opinions?
 
Ice Boy
Ice Boy
12:36 PM
No
 
Committing to a name
Committing to a name
Sure, but I think it is done now ;)
 
Ice Boy
Ice Boy
Just kidding pal :-)
 
Sawarnik
Sawarnik
@Committingtoaname Anyway them, I don't see any moral problem downloading that book.
 
Committing to a name
Committing to a name
"In your scenario you have person A gain $ from bank, and person B lose $ from bank. In my scenario, it is option A: don't download, Person A Gain $0, Person B lose $0, in option B: I download, Person A gain $65 book, person B lose $0" - Me

"Person B loses $65 in the latter case." - Huy

"No he doesn't he simply doesn't gain" - Me

Embodies the argument
 
Chris's sis
Chris's sis
@robjohn I also need to create some applications of my limits. I can tell you for sure they can be applied in many cases I met in the past (that I don't remember right now).
 
Sawarnik
Sawarnik
12:42 PM
@Committingtoaname Hmm, the scenario of a bank is different than a book.
 
Committing to a name
Committing to a name
Sorry I missed where that came from, and I agree by the way:

"So if I'm hacking someone's e-banking account and transfer all his money to my account and use it with my debit card, I'm not creating any loss because the money was never physical, right?" - Huy
 
robjohn
robjohn
@Chris'ssis I am reusing the idea in that summation I showed you yesterday (or the day before) using contour integration.
I will post the answer soon
 
Sawarnik
Sawarnik
@Committingtoaname Ok, don't know what is going on, just to tell that I don't see any moral problem in downloading a book.
 
Committing to a name
Committing to a name
@Sawarnik That's alright :)
 
Sawarnik
Sawarnik
:)
 
N3buchadnezzar
N3buchadnezzar
12:50 PM
mmmmmmmmmmm
 
rehband
rehband
1:13 PM
@Chris'ssis I love these "quickie" problems from Furdui's book. They're mostly doable/easy for me
 
Chris's sis
Chris's sis
@rehband I like them too.
 
The Game
The Game
1:25 PM
Hellu
 
Mats Granvik
Mats Granvik
$$\gamma =\lim_{s\to 0} \, \left(\sum _s -\frac{1}{s+1}\right)$$
Limit[Sum[-(1/(1 + s)), s], s -> 0]
0.577215664901532...
 
Chris's sis
Chris's sis
I posted on main an easy question
0
Q: A cute limit $\lim_{m\to\infty}\left(\sum_{n=1}^{m}\frac{1}{n}\sum_{k=1}^{n-1}\frac{(-1)^k}{k}+\log(2)H_m\right)$

Chris's sisI'm sure that for many of you this is a limit pretty easy to compute, but my concern here is a bit different, and I'd like to know if I can nicely compute it without using special functions. Do you have in mind such ways? $$\lim_{m\to\infty}\left(\sum_{n=1}^{m}\frac{1}{n}\sum_{k=1}^{n-1}\frac{(-...

calculus real-analysis integration sequences-and-series harmonic-numbers
Let's see what answers I receive. :-)
 
The Game
The Game
@Chris'ssis The comments
How is it not cute ??
 
Chris's sis
Chris's sis
@TheGame lolllllllll :-)
 
Sawarnik
Sawarnik
@TheGame What 'sit?
 
The Game
The Game
1:39 PM
@Sawarnik What one
@Chris'ssis As for the 2ns comment he's right
@Chris'ssis It's unclear whether the second member is in the first sum or in the second one or whatever
Add parenthesis
 
Sawarnik
Sawarnik
@TheGame What isit? The pciture?
 
The Game
The Game
@Sawarnik What picture
@Sawarnik Use WASD and arrow keys
 
Sawarnik
Sawarnik
@TheGame s3.neyer.me/ttt
 
Chris's sis
Chris's sis
@TheGame Yeah, OK.
 
The Game
The Game
2 mins ago, by The Game
@Sawarnik Use WASD and arrow keys
 
The Game
The Game
1:54 PM
@Sawarnik TicTacToe ftw
 
Studentmath
Studentmath
Say, I am working over $GF(q)$, and I want to turn $x-y$ to $y-x$
Now, $x-y=x+(q-1)y$, right?
 
Chris's sis
Chris's sis
I just got a new badge for
10
Q: Computing a limit involving Gammaharmonic series

Chris's sisIt's a well-known fact that $$\lim_{n\to\infty} (H_n-\log(n))=\gamma$$ Now, if I change things a bit and use the fact that $\displaystyle \Gamma \left( \displaystyle \frac{1}{ n}\right) \approx n$ when $n$ is large, then I wonder if it's possible to compute the following limit in a closed form...

calculus real-analysis sequences-and-series limits gamma-function
:D
 
rehband
rehband
Lol yeah I just read that thread
 
Masacroso
Masacroso
2:20 PM
guys, there is a way to see MathJax here in the chat? I just see the code
 
Gustavo Montano
Gustavo Montano
 
Masacroso
Masacroso
Thank you
 
The Game
The Game
@Masacroso Yes you can for $5/month. Send me your bank account info right away :P
 
Masacroso
Masacroso
haha... I never hear before about this mechanic with bookmarks, is interesting
 
The Game
The Game
Most browsers can execute JavaScript with bookmarks nowadays
 
Chris's sis
Chris's sis
2:35 PM
No one wants to answer my question :'-(
 
The Game
The Game
@Chris'ssis What one ?
 
Chris's sis
Chris's sis
3
Q: A cute limit $\lim_{m\to\infty}\left(\left(\sum_{n=1}^{m}\frac{1}{n}\sum_{k=1}^{n-1}\frac{(-1)^k}{k}\right)+\log(2)H_m\right)$

Chris's sisI'm sure that for many of you this is a limit pretty easy to compute, but my concern here is a bit different, and I'd like to know if I can nicely compute it without using special functions. Do you have in mind such ways? $$\lim_{m\to\infty}\left(\left(\sum_{n=1}^{m}\frac{1}{n}\sum_{k=1}^{n-1}\f...

calculus real-analysis integration sequences-and-series harmonic-numbers
 
The Game
The Game
@Chris'ssis I thought Achille had in the comments
Isn't his answer ok ? It seems good to me
@Chris'ssis Did you fav your own question ?
 
Chris's sis
Chris's sis
@TheGame Why don't you use his idea to post an answer? I'd like to close the question then ...
 
The Game
The Game
I would feel bad :c
Feels like stealing his idea
 
Semiclassical
Semiclassical
2:40 PM
i've got the answer worked out, based on the same idea as achille hui
but i similarly feel like he's already beaten us to the punch
 
The Game
The Game
@Chris'ssis Why don't you answer your question ?
 
Semiclassical
Semiclassical
but i similarly feel like he's already beaten us to the punch
 
The Game
The Game
@Semiclassical er ...
 
Semiclassical
Semiclassical
ugh
kept getting a timeout/retry message
 
user2179021
user2179021
2:53 PM
hi
has anyone got any ideas for how to solve math.stackexchange.com/questions/952446/… even in 3d?
 
The Game
The Game
@user2179021 How do you know what the OP meant by 'region' ?
@user2179021 Or, is it you with another username ? -__-
 
user2179021
user2179021
I think it's clear from the pizza slice example isn't it?
what do you think it should be called?
why don't we edit it with a better explanation?
 
The Game
The Game
@user2179021 It's not clear at all for me in n dimensions
I don't wanna try to answer a question with unclear notations :c
That is probably why no one has answered yet btw
 
user2179021
user2179021
ok.. so I think I understand what it means :)
in order to get from one region to another you have to cross a hyperplane
 
Chris's sis
Chris's sis
@TheGame see @robjohn's answer
1
A: A cute limit $\lim_{m\to\infty}\left(\left(\sum_{n=1}^{m}\frac{1}{n}\sum_{k=1}^{n-1}\frac{(-1)^k}{k}\right)+\log(2)H_m\right)$

robjohn$$ \begin{align} \lim_{m\to\infty}\left(\sum_{n=1}^m\sum_{k=1}^{n-1}\frac{(-1)^k}{nk}+H_m\log(2)\right) &=\lim_{m\to\infty}\sum_{n=1}^m\sum_{k=n}^\infty\frac{(-1)^{k-1}}{nk}\\ &=\sum_{n=1}^\infty\sum_{k=n}^\infty\frac{(-1)^{k-1}}{nk}\\ &=\sum_{k=1}^\infty\sum_{n=1}^k\frac{(-1)^{k-1}}{nk}\\ &=\sum...

That one is the way to go.
 
The Game
The Game
2:59 PM
@Chris'ssis hmm I see
 
user2179021
user2179021
robjohn rocks
 
The Game
The Game
@user2179021 Let's go back to 2D. To go from a 'slice' to another you need to cross a line ??
What do you mean by 'cross' ?
 
user2179021
user2179021
take any two points in different regions, there exists a point on a hyperplane on the straight line between them
@Ge
@TheGame sorry.. I am not good at adding the @ part :)
 
The Game
The Game
@user2179021 How do you define the straight line between two regions ?
 
user2179021
user2179021
@TheGame it is a straight line between points I think
@TheGame take any two points in different regions
@TheGame does that make sense now?
 
The Game
The Game
3:05 PM
@user2179021 You're unclear :/ Are you trying to say that two regions cross something iff there exists two points, one in each region, so that the line through those points goes through that thing ?
 
user2179021
user2179021
@TheGame no sorry. I am saying that two points are in different regions iff the straight line between them contains a point in a hyperplane
@TheGame this should then define an equivalence class for points which should define the term region
 
The Game
The Game
@user2179021 Again, what are hyperplanes in 2D ?
for n=2
 
user2179021
user2179021
@TheGame hyperplanes in 2d are lines
 
The Game
The Game
exactly
So imagine a pizza slice
Take two points in that region
Obviously the line between then intersects a third line
That would mean that the two points are in different regions, according to your definition
 
user2179021
user2179021
ah.. the problem is if the pizza size covers > 180 degrees
then my definition doesn't work
if it is less than 180 degrees the straight line between any two points doesn't intersect any other line
hmm. not sure how to fix the > 180 degrees problem
 
The Game
The Game
3:11 PM
@user2179021 It does ! come here i'll try to draw something twiddla.com/1786969
 
user2179021
user2179021
i am there
 
anorton
anorton
This is the second answer this user has posted like this: math.stackexchange.com/a/952639/23353 :\
 
The Game
The Game
@user2179021 Done
 
user2179021
user2179021
@TheGame ok I see your lovely picture and I see the confusion. there are 2 lines that define the red region . So in this case k = 2. First the lines should go all the way through the origin. Second the blue doesn't doesn't intersect either of the two red lines.
@TheGame I am not sure why you added a third line through the origin there
 
The Game
The Game
The green line is the hyperplane
 
user2179021
user2179021
3:16 PM
@TheGame what is k in your example?
 
The Game
The Game
I'm not even talking about $k$, i'm just trying to understand what you meant by 'two points are in different regions iff the straight line between them contains a point in a hyperplane'
 
user2179021
user2179021
@TheGame If k = 1 then those two blue dots are NOT in the same region. The two regions created by the green hyperplane are up and left and down and right from it
@TheGame but I am not sure what the red region you have drawn is now
 
The Game
The Game
The red region is the pizza slice (2D cone)
 
user2179021
user2179021
@TheGame OK so the pizza slices are caused by hyperplanes. So in your case you would have to have 3 hyperplanes I suppose and extend the two red lines
@TheGame in which case the two blue dots are still NOT in the same region
@TheGame let me see if I can draw too :)
 
The Game
The Game
@user2179021 wait it seems that we aren't talking about the same thing
Let me recap
The question starts by ''For a n dimensional space, what is the maximum number of n dimensional regions"
So first i was trying to get what those regions were
Hence i drew one for n=2
That's the pizza slice
@user2179021 I think it would be better if you could reformulate the OP's question, it's unclear in english.
I guess that's whence all the confusion comes from
 
user2179021
user2179021
3:21 PM
@TheGame drawn :)
@TheGame can you see my new picture?
 
The Game
The Game
In his question the space of 'when' and 'where' lead to bad understanding
 
robjohn
robjohn
@Chris'ssis: I just saw that this morning I answered a question that was in a letter from Ramanujan to Hardy. I got the same answer :-)
2
 
The Game
The Game
@user2179021 I can
@user2179021 I understand what you meant now, but could you please rewrite the OP's question so that it's clear ?
 
user2179021
user2179021
@TheGame ok.. so what is the answer for 3d? :)
 
The Game
The Game
@user2179021 >:o I'm telling you, I can't give an answer unless you rewrite his question
 
user2179021
user2179021
3:24 PM
is it clearer now?
It seems he already rephrased it
maybe he is watching us :)
 
The Game
The Game
:) let me see
ooooh
Now it's clear :D
 
user2179021
user2179021
hooray!
for 3d my guess is that you get 1, 2, 4, 8, 12 for the number of regions
but I am really not sure
 
The Game
The Game
Aren't hyper planes of a space of dimension $n$ all of dimension $n-1$ btw ? (i'm not sure)
 
user2179021
user2179021
yes
 
The Game
The Game
Then no need to add that in the question :)
 
user2179021
user2179021
3:26 PM
:)
well. no.. you can have hyperplanes of lower dimension
they just don't separate things in the way you would want
 
The Game
The Game
Ah ok then
 
user2179021
user2179021
i mean points exist in 3d
for example
that's a 0-d hyperplane in 3-d :)
 
The Game
The Game
@user2179021 How do you define the dimension of a region ? The number of independent vectors required to span it, I guess ?
@Chris'ssis Titans are back
 
user2179021
user2179021
@TheGame right
 
The Game
The Game
@user2179021 So to make sure I understood it let's go back to n=2. According to you, what is the answer in that case ?
 
user2179021
user2179021
3:29 PM
1,2,4,6,8,10
as it says in the question
no hyperplanes given one region
1 gives 2 etc.
 
The Game
The Game
Ok all right
Now for n=3
k=1 gives 2
 
user2179021
user2179021
well you get 1, 2, 4, 8 and then 12 I think
but I am not sure about 12
 
The Game
The Game
k=2 gives 4
k=3 gives .. how do you get $8$ ?
I get $7$
 
user2179021
user2179021
I am just slicing perpendicular to the other two hyperplanes
 
The Game
The Game
k=2 -> two perpendicular
k=3 -> two parallel one perpendicular ?
Is that so ? @user2179021
 
user2179021
user2179021
3:34 PM
in 3d you can three orthogonal hyperplanes going through the origin
you can have
 
Wildhorn
Wildhorn
Anybody here can tell me what is the matrice of a 6 sided dice?

I am trying to multiply 1d6 matrice with another 1d6 matrice, but I am not sure of how they are shaped
is it simply {1,2,3,4,5,6} ?
 
The Game
The Game
@user2179021 OOhh my bad, my drawing screwed up
 
user2179021
user2179021
:)
 
The Game
The Game
@user2179021 According to you, what would it be for k=5 ?
@user2179021 14 ?
 
user2179021
user2179021
after 8 comes 12 I think but I am not sure
I have to go.. chat another time
 
The Game
The Game
3:43 PM
Okay, have a good day/evening
 
robjohn
robjohn
@Wildhorn I am not sure what you mean. What is the purpose of this matrix?
 
Wildhorn
Wildhorn
I want to know the probability of each possible result
 
Masacroso
Masacroso
he is talking about the representation of a generating function as a matrix
 
The Game
The Game
@robjohn Do you have an answer for my question here math.stackexchange.com/questions/952137/… that does not use ideals ? I have never seen those, so it would bother em to accept an answer which uses theorems I have never seen :/
 
Chris's sis
Chris's sis
3:59 PM
@robjohn however ...
$$\lim_{N\to\infty}\left(\frac{1}{2}\sum_{n=1}^{N}\frac{H_n^3+H_n^{(3)}}{n}\sum_{k=1}^{n-1}\frac{(-1)^k}{k}+\frac{\log(2)}{2}\sum_{n=1}^{N}\frac{H_n^3+H_n^{(3)}}{n}\right)\neq\operatorname{Li}_5\left(\frac{1}{2}\right) $$
 
robjohn
robjohn
@TheGame you have not had abstract algebra? That is where ideals are dealt with.
 
The Game
The Game
@robjohn I have studied vector spaces, but as I am in PC (physics-chemistry) and not in MP(math-physics) we do less maths than the latter, and do not study algebras, groups etc a lot.
 
Rajesh D
Rajesh D
Hi @Rob
 
Wildhorn
Wildhorn
4:16 PM
@Masacroso told me to forget matrice and go with polynomial instead...

So I got f(x)=(2x^0+x^1+x^101+x^2+x^202)^2

How do I translate that to computing language? like Javascript?
 
Sujaan Kunalan
Sujaan Kunalan
Does anyone know if "linear space" is just a synonym for "vector space" ?
 
robjohn
robjohn
@RajeshD hey there... how are things?
 
Rajesh D
Rajesh D
fine cool going
@robjohn : Do you have any acquaintance with functions of bounded variation in more than 1 dimension?
 
robjohn
robjohn
@RajeshD I've heard of bounded mean oscillation (BMO), but I am not sure how one would define bounded variation in more than one dimension.
 
Rajesh D
Rajesh D
there are about 7-8 definitions starting from Hardy and Arzela to modern and currently accepted definition by Griorgi which is in terms of distributions
 
robjohn
robjohn
4:30 PM
@RajeshD would these be similar to Lipschitz spaces?
 
Balarka Sen
Balarka Sen
@Huy Never watched the movies. Read the book.
 
Rajesh D
Rajesh D
@Robjohn
 
robjohn
robjohn
@Wildhorn for a polynomial, I would say $x+x^2+x^3+x^4+x^5+x^6$ for a six sided die.
@RajeshD okay, so they are the same.
 
Sawarnik
Sawarnik
@Nick You know topology?
lol
 
Rajesh D
Rajesh D
@Robjohn But interesting to see this mathoverflow.net/q/181914/14414
 
Wildhorn
Wildhorn
4:40 PM
@robjohn it is not a normal d6. Values are {0,0,1,101,2,202}

Which gives f(x)=(2x^0+x^1+x^101+x^2+x^202)^2

But I need a way to translate that in Javascript language
 
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