Hi all, sorry to interrupt/bother, but does anyone know if the converse of the following statement is true? If X is an irreducible topological space, then the constant sheaf Z is flasque.
@KevinDriscoll Well, you can go the other way around. Pick an open set $U$ containing a point $x$. Then $X\setminus U$ is closed and disjoint from $x$... =)
:O I'm just new @KevinDriscoll I've seen the $X \backslash U$ somewhere in my book and that's the complement definition... with elements in X, but not in U
Ok I have this function $$f(x)=\begin{cases} 1& x=\frac{1}{n}\\ 0 (other)\end{cases}$$. How is $f:[\frac{\epsilon}{2},1]\rightarrow\mathbb{R}$ a constant function?
@KevinDriscoll What I am saying and asking (simultaneously), is could the problem of finding an equation to figure out the number of combinations of N digits with the rules you see using Binary Bitshifts and Addition?
Hi all, I have the following problem. I can easily show that the constant sheaf Z on an irreducible topological space X is flasque, but I am wondering if the converse is true. Namely, does the constant sheaf Z being flasque imply that X is irreducible?
@alex here's the list of all the topics I should know
Basic definitions, matrix coefficients, Schur orthogonality, invariant inner products and complete reducibility of representations, characters of finite groups and parametrization of complex representations by characters, character tables, Peter-Weyl theorem.
I seem to vaguely remember parts of all of that except for PW from my $S_n$ representations course
@Chris Ya when you say combinations the 2nd example you gave is excluded by definition, but not the first
I don't see the obvious answer, so I'd post on main @ChrisOkyen but try and be very clear about the problem you're trying to solve. Its not obvious initially from your pastebin
So what your are saying @KevinDriscoll is the first examples 11 may not be known or understood as being defined as repetitious as 123 -> 321 and I should be careful to specify this on main
I feel chat is a better place over all for me becuase I don't always specify right and in forums we go back and forth clearing stuff up for a long while.In chats its quicker and wont get me donwvoted for not being clear
i have to show that if $P_n(x)$ is the interpolating polynomial for $e^x$ at the points $\{j\frac{b}{n}|j=0,\ldots, n\}$, $$\lim_{n\to\infty}\operatorname{max}_{x\in [0,b]}e^x-P_n(x)=0$$
I get the concept about mean growth annual rate, but I am curious -- when calculating it, after the rates are multiplied, why does one raise it to the 1/n power? Where n is the number of elements
@LitheOhm what it really comes down to is that you're taking a type of average, a geometric mean. you're used to taking averages by summing and then dividing by n=number of terms. with rates, you're multiplying and then square rooting by # of terms.
I'm quite excited by it. My bookshelf has a bunch of math books on it, Taleb, Mlodinow, etc.
I actually dropped in here because some students asked for help on the school discussion forum and I could explain all the stuff, save for the geometric mean part lol. Still a bit green I suppose, but meh :)
@PedroTamaroff I'm not so sure there's much difference. Being beautiful and being skilled at sports (or math) aren't so different. It requires a combination of the right environment, the right talent, and consistent practice.
