@SteamyRoot no clue. I was trying to hit backspace when editing, it caused my browser to back a page and when hit the forward button and went back to the page the symbol mysteriously appeared in the edit box.
For example $m=5$ (1/5 construction of a cantor set looking self similar set) $$G(x)=\frac{1}{5^{N_x}}+\frac{1}{5}\sum_{n=1}^{N_x-1}\frac{a_{nx}}{5^n}$$?
I understand, and my question is why is it considered a nessecesry background? I actually like the material but it haven't helped me that much in understanding higher level math
@AkivaWeinberger there are several characters like that, but this doesn't seem to render to any width. In the edit box it looks like a square with two rows of digits "00 08".
It has great trolling powers. Like, on many online forum/messageboards, the title you type becomes the link used to access the topic. So if you put the title full of those symbols, the link is invisible and nobody can click it.
We knew that the cantor function is constructed iteratively by taking away the middle thirds of each segment. This can be generalised to e.g. taking away the middle 5th s of the segments. What happens to the cantor function as my nth where n grew without bound. Naively I seemed to expect to get the line y=x, but attempt to prove it using the series I wrote above just give me a bunch of zeros?
So there should exists a family of self similar cantor like functions which is constructed by taking the middle e.g. 1/4, 1/5, 1/6 etc. of each segment away
O wait a sec... I got $\lim_{m\to \infty}G_m(x)=x$
@zee Do we expect as the constant intervals in each iteration of the construction of a cantor like function become smaller, the function will tend towards the function y=x?
Coudl someone explain to me why here: https://math.stackexchange.com/questions/9580/linearity-of-convergence-in-distribution-of-random-variables $X \to X_n$ in distribution. It seems really wrong to me =(
Let $S$ be a closed surface of genus $g > 0$ and $[S,S] = Hom(\pi_{1}(S),\pi_{1}(S))$ be the monoid of (homotopy classes of) continuous maps from $S$ to itself.
Consider the sub-monoid of elements that induce the $0$ map on $H_{2}(S,\mathbb{Z})$. Question Is there a "nice" set of generators for...
There's a theorem of Kneser that says maps of closed oriented surfaces of degree 0 are homotopic to non-surjective maps, so this is equivalent to saying your map factors through the 1-skeleton, aka you're trying to get a nice set of generators Sigma_g -> Sigma_g that factor as maps pi_1(Sigma_g) -> F_{2g}
I think that should be a feasible classification if you can understand a little bit better what the image can be; it's necessarily of infinite index, say
In general I think you should be able to prove that up to a diffeomorphism of the surface the map factors through the handlebody
I'll have to write a short thing about Frobenius theorem for an uni project this semester, looks rather interesting (not the one Akiva mentioned though)
Hey, small question here : what are the main fields in Linear Algebra, which are important for Computer Science, especially machine learning and neural nets?
Anyway, uh, I'm not sure how many levels this will go before the intended recipient is revealed, so in order to not find that out, it's seems fun from a very brief taste, but it's early to say
@AkivaWeinberger hint: multiply a bunch of numbers together and subtract 1. Is the result not coprime to all the original factors? Dare I not conjecture, that the same is true for polynomials?
Let $S$ be a closed surface of genus $g > 0$ and $[S,S] = Hom(\pi_{1}(S),\pi_{1}(S))$ be the monoid of (homotopy classes of) continuous maps from $S$ to itself.
Consider the sub-monoid of elements that induce the $0$ map on $H_{2}(S,\mathbb{Z})$. Question Is there a "nice" set of generators for...
