@JM that's usually the time I spend reading a book, but this time was more productively spent :-)
@Ilya Unfortunately I was on the mobile interface, so it was hard to see what questions he had answered. When I finally found some questions that I hadn't seen before, his rep was capped.
@robjohn being romantic is smth I don't want to lose ever. I would even sacrifice wisdom for this if needed - otherwise I think the life will lose its colors
@robjohn I agree - that's why I'm talking about lobes only. Sitting in tattoo/piercing saloon and waiting for the master, we were just looking around, seeing all these pictures with pierced penises etc.
When we were returning from Spain, we were staying in the queue and the guy before us was full of piercings (like monstrous tunnels in ears, pierced lips, nose, eyebrows). My wife felt uncomfortable, but that was still ok for me unless I've seen that he has a piece of metal hidden in his arm under the skin :-!
so I had to focus myself and her on something else because we couldn't escape the queue
@robjohn )) that's nice. Sorry, I have to go to the library to receive the library card and take a look if they have some Russian literature there. I'm missing it
@JonasTeuwen If I would like to learn something about Choquet theory (or to get at least some basic overview), do you have some good book recomendation?
Hmm. I'm not too sure, but I think if the ellipticity is uniform, it shouldn't matter that the coefficients vanish at a point if they are smooth. I will have to think on this.
Hello, is there some common notation in mathematics for coordinatewise product of two vectors? { (x1,...,xn), (y1,...,yn) } |-> (x1y1,...,xnyn). In Matlab it is x.*y
Is there a notation for element-wise (or pointwise) operations?
For example, take the element-wise product of two vectors x and y (in Matlab, x .* y, in numpy x*y), producing a new vector of same length z, where $z_i = x_i * y_i$ .
In mathematical notation, there doesn't seem to be a standard ...
This is a notation question. Assume one is given two vector $\mathbf{a}$ and $\mathbf{b}$, and one constructs a third vector $\mathbf{c}$ whose elements are given by
$$c_k=a_k b_k$$
Is there any standard notation for this simple operation?
Is the notation below acceptable?
$$\mathbf{c}=\mathb...
@JonasTeuwen: Regarding what I said about Pangasius yesterday: I think you still have the wrong picture of what it's like here. So let me expand:
ETH is a factory where they produce cattle ("students"). At noon they drive the cattle into a hall and feed it. The catering is outsourced to some company. This company drives to the tip at night picks up all the garbage, shreds it, ads colour and flavour, presses it into shapes of cauliflower, spaghetti and nameless shapes and then serves it to the cattle the next day.
@Matt You should be aware of the fact that you're complaining on a pretty high level there. I agree that the Mensa isn't brilliant, but, as a matter of fact, the ETH/Uni Mensas are quite decent compared to what I've seen everywhere else.
@tb I can't help it, the high level just happened. I have nothing but bad memories about CH and ETH in particular. Cafeteria is just one tiny part. One of the parts that I can still see with humour.
I have looked through some of the previous questions posted on this topic, and I think mine is different.
Is there a flaw in DEFINING division by zero? For example, define
$\frac{a}{0} = \infty_a$
it would seem like things work now, for example,
$\frac{a/0}{b/0}=\frac{\infty_a}{\infty_b}=...
At least I've learned never to answer a question from picakhu again.
although I got two downvotes for posting a correct answer.
Someone else posted the same answer as me at the same time (but they unfolded the proof that x*0 = 0 into it) so I would have happily deleted mine if it hadn't been downvoted..
Matt, and one more suggestion. Sometimes, its better to avoid symbols. Have you considered getting rid of \mid altogether and say $|\phi(G)|$ divides |H|.
$|\phi (G)| {\large |} |H|$ that is what I was really trying to remember. you can use \large or \Large This construct allow more than one character to be enlarged.
Yes, I wanted to point out: the smaller text gets pushed down. This is ok in some cases, but in Matt's example, the phi(G) and |H| were somewhere below, and the big vertical sign wasn't symmetric.
Bloody H. I've just realized that almost a year I was solving Bellman equations which are honestly speaking Dirichlet problems for Laplace equations. And whom of these three guys should I acknowledge now when I write the paper? they are all even from the different countries
I like your answer, robjohn and there's nothing wrong with undeleting it, IMO. I can't understand why people like the other answer. Unjustified and more complicated.
Yes, actually, I think you should undelete the answer. When the question is simple, I guess that it's a good thing to look for the "best" answer possible.
Let $f(x)$ be a monotonic function on $[0,\infty)$ and for every $x>0$ it is integrable in $\lim_{x\to \infty}\frac{1}{x}\int_{0}^{x}f(t)dt=a$. I need to prove that $[0,x]$ so that $\lim_{x\to \infty}f(x)=a$.
I tried to use the limit definition:
$|\frac{1}{x}\int_{0}^{x}f(t)dt -a|<\epsilon...
@tb I have the Halmos book about writing mathematics. Were you serious that this is a good book or did you only think it was funny because of the TU Delft link (they have sent it through internal mail :D).
@robjohn So, let me get this. You posted your answer, Hardy posts an answer after you, then he goes and asks in a separate thread what you answered and then writes "It's beginning to look as if this should be closed as a (nearly?) exact duplicate. I was moved to ask this by an earlier similar question posted today, but the answers getting posted there make it appear that it's being treated as if the questioner meant just what I asked here."
@QED Did you really make this up yourself about division by 0? " since the dawn of precalculus mankind has been obsessed with finding a way to perform that forbidden division..."
@Srivatsan I agree, but this obsession with 0 and infinity is what fuels my interest in math ... I think it is because of the book I read when I was young called "From Zero to Infinity" have you read it?
My question is very simple: Are there any interesting examples of number theory showing up unexpectedly in physics?
This probably sounds like rather strange question, or rather like one of the trivial to ask but often unhelpful questions like "give some examples of topic A occurring in relation ...
This is a notation question. Assume one is given two vector $\mathbf{a}$ and $\mathbf{b}$, and one constructs a third vector $\mathbf{c}$ whose elements are given by
$$c_k=a_k b_k$$
Is there any standard notation for this simple operation?
Is the notation below acceptable?
$$\mathbf{c}=\mathb...
I have looked through some of the previous questions posted on this topic, and I think mine is different.
Is there a flaw in DEFINING division by zero? For example, define
$\frac{a}{0} = \infty_a$
it would seem like things work now, for example,
$\frac{a/0}{b/0}=\frac{\infty_a}{\infty_b}=...
Let $f(x)$ be a monotonic function on $[0,\infty)$ and for every $x>0$ it is integrable in $\lim_{x\to \infty}\frac{1}{x}\int_{0}^{x}f(t)dt=a$. I need to prove that $[0,x]$ so that $\lim_{x\to \infty}f(x)=a$.
I tried to use the limit definition:
$|\frac{1}{x}\int_{0}^{x}f(t)dt -a|<\epsilon...
