Mathematics

@TedShifrin Ok, again. Am I wrong when I reassure you in the presence of such point in $\mathbb{Q}$?

Yes.

@TedShifrin Yeah, they talk a lot about the red book.

@MikeMiller Is it for me?

Yeah.

8:02 PM

@MikeMiller Can you please come up with a counterargument?

Let $a_n$ be $\pi$ out to $n$ decimal places, and let $b_n$ be $a_n + 10^{-n}$. Then the only element in $\Bbb R$ in every $(a_n,b_n)$ is $\pi$. There are no rationals there.

In particular, the intersection in $\Bbb Q$ is empty.

To see why this shouldn't be true, look at the proof for $\Bbb R$ and see where it uses a property special to $\Bbb R$.

Sorry, I can't edit, but those intervals should be $[a_n,b_n]$.

@MikeMiller But nevertheless. You can name me $\forall \varepsilon >0$ and I am still able to give you a common point.

@mikeonly what do you want to say with this precisllely?

@evinda: How's it going?

@MikeMiller The expansion works however rigidly when there are intervals of finitesimal length.

8:12 PM

@amWhy: Hi to you too. You've been away for a long time. :D

@quid Frankly saying, I see no global use in this discussion now except for revealing my weak spots before an exam which is great. :) But by saying that, I mean I can give you a formula of a common point in terms of $\varepsilon$.

robjohn

@TedShifrin Hey, Ted! I've been offline watching the Rose Parade (and now some games).

Thanks @mikeonly, I do not understand that either, but I will not insist.

Shockingly, Martin Sleziak is not a room owner in Tagging room. The only owner is Eugene, who was last seen in March. I suppose moderators can add room owners... @robjohn?

Could you make Martin a room owner there?

robjohn

@Behaviour is there a need to have a room owner there?

8:19 PM

Martin asked for a feed of [tagging] tag to be added to that room. Not being RO, he can't do it himself.

does this make sense to you? math.stackexchange.com/a/1087816/33907

So either it's a mod action to make him RO, or a mod action to change feeds every time something like this comes up.

@quid are you active on mse?

It was a pleasure to discuss this topic with you, thanks. :)

@Huy Fine, and you? :)

8:20 PM

@evinda: Yeah, just a bit bored so I started watching Skyfall again. :D

@evinda: What are you up to tonight?

@JorgeFernández what do you mean by mse?

mathematics stack exchange

I remember you answered one of my first questions on MO

@Huy Aha :D I want to learn something, about I still don't know which subject. :/

@evinda: What are you interested in?

@evinda: What subjects have you already studied?

@Huy You mean now in the vacations or generally?

8:24 PM

@evinda: Generally.

@JorgeFernández I am a bit more active here lately. (I was not sure at first if you meant this site or meta.SE) Not very active. But top 100 or so last month.

I just checked the question you mentioned. :-)

It was this one mathoverflow.net/questions/124116/…

@Huy So far I have took 29 subjects... I had for example Calculus, Analytic Geometry, Linear Algebra, Intoduction to programming, Number theory, Applied Maths and so on... I liked the most of them.. What are you interested in except from Differential Geometry?

although you didn't answer it, but for some reason I remembered you more than the person who actually answered it.

@evinda: I haven't really studied differential geometry yet. :D

8:28 PM

@user153330 Hmm. I didn't really learn it from anywhere. It was my own program. I can show you the essence of how it works.

@evinda: And what are you interested in?

@evinda: Anything on particular you'll want to be able to do or understand?

I need to learn generating functions urgently

@JorgeFernández oh that one! I was looking at one that I really answered

oh, I didn't remember that for some reason.

is it considered wrong to edit your best posts once in a while so they surface and get upvotes?

@Huy I like computer science that's why I choose this field but I also like other subjects like Set Theory and Number Theory.. What are you interested in?

8:35 PM

@evinda: Mostly mathematical physics.

@evinda: Have you studied complexity?

@JorgeFernández depends. One should certainly not overdo it.

@Huy Do you mean complexity of algorithms?

I did it today for the first time with an answer I answered half an hour ago which no one paid attention too.

@evinda: I'm not sure what you mean. I've never heard the word complexity being used with algorithms. Usually, you can compute the runtime of an algorithm, say it is $O(n)$, but that's not something I mean. I mean e.g. finding out whether a problem is solvable in polynomial time.

@Huy No, I just have seen the time complexity of algorithms, which is the runtime of the algorithms :/

8:41 PM

@evinda: en.wikipedia.org/wiki/Computational_complexity_theory

@Alizter how did you implement it in visual basic?

@evinda: That's the only topic from theoretical CS that I actually enjoyed. $P \neq NP$ is a well-known conjecture of complexity theory.

@user153330 I didn't use visual basic, I used C#

@Alizter oh, so please show me the essence then : )

@Huy Next semester I will take the subject Algorithms and Complexity.. Maybe we will see it there...

8:43 PM

@evinda: Most definitely.

@evinda: Well, that's the only thing in CS I liked. There's nothing else I could recommend you from my own experience. :D

Aha :D @Huy

@evinda: Do you like physics?

@Huy I wrote a high grade, but I don't like it so... You?

Lol visual basic

@evinda: I like it. :P

@evinda: How come you have already taken 29 subjects and are still in your BSc? With that amount of subjects I'd be starting my PhD already.

8:46 PM

@user153330 I take a group and label the elements 1...n then I assign colours to them chromatically. Each point of the table I compute which element it would correspond to. For example, cyclic groups are easy: I take element i and element j and I know that the operation will give me element i + j with special cases handled. So when I want to compute the operation on any two elements I essentially have a function that will take the labels and give me the label for the result.

@Alizter where did you learn C#?

@user153330 Permutation groups were a bit harder but I ended up converting labels to matricies. Multiplying the matricies and then finding the label for the corresponding matrix.

Hi @Alizter

Mary Star

@Huy At the following $$\sin^2(x) = \sum_{k=0}^\infty (-1)^k \frac{x^{2k+1}}{(2k+1)!}\cdot \sum_{k=0}^\infty (-1)^k \frac{x^{2k+1}}{(2k+1)!}=\sum_{k=0}^\infty \sum_{i+j=k}(-1)^i \frac{x^{2i+1}}{(2i+1)!}(-1)^j \frac{x^{2j+1}}{(2j+1)!}=\sum_{k=0}^\infty \sum_{i+j=k}(-1)^{i+j} \frac{x^{2(i+j)+2}}{(2i+1)!(2j+1)!}$$ isn't the second equality the Cauchy product??

@user153330 I taught my self from books in the library and the internet

You don't need to do it in C#

Hi @BalarkaSen

8:47 PM

okay thanks ^^^

@BalarkaSen How was your new year?

Come with me to the NT room, @Alizter

@user153330 No problem.

Way too much crowd here

@BalarkaSen OK. starts spinning

8:48 PM

@Huy We have to take in total 240 ECTS.. If I pass all the subjects this semester I will have 182 ECTS...

@evinda: And how many ECTS points does a subject usually grant?

That's around 6 on average, by my mighty calculations.

@amWhy I'm a bit curious, why did you reject this suggestion?

@Huy Yes, it can be 6/7/8..

@evinda: Interesting. Do you have to write a thesis?

Don Larynx

►

8:51 PM

@Huy Only if I want to.. But I don't think that I will write.. When will you write your thesis?

@evinda: Probably next year.

@Huy At which subject?

@NajibIdrissi I think you may have put in more detail than necessary.

@MikeMiller I don't think so, compare with other tag wikis

@evinda: Something in quantum field theory, most likely.

Alec Teal

8:56 PM

Null set in the basis of a topology, y/n

@evinda: Will you do all of your studies at your current uni or are you planning to go to a different uni at some point?

You intend to do a PhD in physics, @Huy?

@NajibIdrissi OK, after looking at some others, I agree.

@Huy I think that I will continue my studies at my current uni.. What's with you?

Will you continue after the master? @Huy

A tag-wiki can be really long. A tad-wiki excerpt must be short. (But this is sw evforced anyway).

I approved it @NajibIdrissi. And Hi! I never saw you in chat so far.

@quid Hi, thanks! I'm here sometimes, mostly I forget it exists

9:01 PM

What, precisely, does mathrel do?

@MikeMiller It changes the spacing so that it's spaced like a relation

There's mathbin, mathop and mathrel

hmm

Q: What is the difference between \mathbin vs. \mathrel?

34

These seem to be very similar as they both separate two operands. When would one be used over the other? Is there any difference in the math spacing surrounding them? How would the spacing in these relate to to the spacing produced by \mathop?

math-mode

It's veeeery subtle TBH

OK, I give up. Why is this tagwiki broken?

That's not how you use mathrel, it should be \mathrel{\middle{|}}

(oh and thanks for the approve on the tag wiki)

9:06 PM

Doesn't seem to fix it.

And no problem.

I don't know if mathjax has \middle, as far as I remember you need to load some package in LaTeX to get it

Hm, still broken

The thing is that it breaks even if you remove that whole thing.

Found it

Didn't find it

That's weird, it compiles in LaTeX if you remove the \middle

Mary Star

$P$ uniform distribution on $[0,1]$.
$$A_n=\bigcup_{i=1}^{2^n-1} \left [ \frac{2i-1}{2^n}, \frac{2i}{2^n} \right ], n \in \mathbb{N}$$

To calculate $P(A_n)$ do we have to do the following??

$$P(A_n)=P \left ( \bigcup_{i=1}^{2^n-1} \left [ \frac{2i-1}{2^n}, \frac{2i}{2^n} \right ] \right )=\sum_{i=1}^{2^n-1}P\left ( \left [ \frac{2i-1}{2^n}, \frac{2i}{2^n} \right ] \right )=\sum_{i=1}^{2^n-1} \left ( \frac{2i}{2^n}-\frac{2i-1}{2^n} \right )=\sum_{i=1}^{2^n-1} \frac{1}{2^n} =\frac{1}{2^n} \sum_{i=1}^{2^n-1} 1=\frac{2^n-1}{2^n}$$

Don Larynx

gonna go watch my uni kick butt, see you all later!

9:10 PM

not your butt, surely, @Don?

Don Larynx

uh...right

Mary Star

Or is it $$P(A_n)=P \left ( \bigcup_{i=1}^{2^n-1} \left [ \frac{2i-1}{2^n}, \frac{2i}{2^n} \right ] \right )=\sum_{i=1}^{2^n-1}P\left ( \left [ \frac{2i-1}{2^n}, \frac{2i}{2^n} \right ] \right )=\sum_{i=1}^{2^n-1} \frac{1}{\frac{2i}{2^n}-\frac{2i-1}{2^n}}=\sum_{i=1}^{2^n-1} 2^n=2^n(2^n-1)$$ ??

If you look at the preview in the box, the problem becomes apparent: Markdown eats backslashes before figure braces.

@MikeMiller @evinda: I'd love to do a PhD after my MSc but I doubt I have what it takes.

If you double the backslashes (escaping them from Markdown), the formula works.

9:14 PM

@Behaviour Maybe it becomes apparent to you!

Why do you think so? @Huy

@MikeMiller: If I was doing a PhD after my MSc, that would still be in mathematics. All I do is officially contributing to my MSc in mathematics, even though half of the subjects are physics subjects.

@Huy So I guess the question I wanted to ask was: you're doing an MSc in physics?

@MikeMiller: I think that question just got answered? :P

What does not become apparent is why MathJax-Markdown interaction is different on tag wiki page.

9:15 PM

Yes.

@evinda: I'm not half as gifted or ambitious as many students at my uni, and I don't want to go to a less popular university to do a PhD.

@MikeMiller: Actually, so far, only QM2 and GR will be counting towards my MSc. Maybe I'll take something on QFT or String Theory too, but I don't know if I have the time.

I was just surprised that those are considered part of a math MSc.

It's very weird, apparently the renderer in the preview for tag wikis doesn't work the same as the usual renderer

Weird that physics requires so much differential/geometric part of mathematics than the algebraic part

@MikeMiller: We can choose from a lot of different subjects counting towards our MSc. GR is officially a subject any maths MSc can choose, for QM2 however I had to write an e-mail to get permission for it to count towards my math MSc. The lectures are meant for physics MSc.

9:18 PM

That makes sense.

I didn't want to double the backslashes, though (since that would break if the rendering reverts to normal). Replaced backslash-braces by \lbrace and \rbrace. Works now.

@MikeMiller: Here you can see all courses any maths MSc can take as a core or elective course. There are other kinds of courses too. =)

lol

Your link's broken, anyway. Don't worry about it.

I can't believe I had to go through every possible combination until I got it right.

oh, now it's fixed.

9:22 PM

Who invented this kind of syntax for posting a link? Madness.

OK, so your MSc really does allow a lot of physics overlap. I think that's rare here.

Should tag excerpts start with a capital or not? None of them do on stackoverflow, but here it's almost 50-50

I don't think it matters, nor do I think we should care enough to make it consistent.