The zero vector is defined as simply the vector consisting of pure zeros as elements. It is labeled as the number zero with an arrow above $\vec 0$ or as ...

I was tring to culculate the fundamental group of $\mathbb{RP}^n$ with VAN KAMPEN to have a better understanding on how to use this theorem. $\left(\mathb...

It's usual in Complex Analysis see some points of the domain of a function as undefined. See for example as Wikipedia defines a removable singularity...

In Wikipedia, there is Shannon's proof on Nyquist-Shannon sampling theorem. ( http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem#S...

My book gives the following definition: Let $(M,d)$ be a metric space, and let $\mathcal{T}$ be the collection of all subsets of $M$ that are open in the ...

I'm drawing certain cases to better understand some of the jargon in introductory Topology. Can you guys quickly tell me if the four statements I mad...

If $S = x+x^{2}+x^{4}+x^{8}+x^{16}\cdots$ Find S. Note:This is not a GP series.The powers are in GP. My Attempts so far: 1)If $S(x)=x+x^{2}+x^{4}+x^{8}+x^...

I came across the following word problem related to divisibility: In a certain town 2/3 of the adult men are married to 3/5 of the adult women. Assume tha...

Given the vector field $\vec{F}(x,y) = (x^2+y^2)^{-1}\begin{bmatrix} x \\ y \end{bmatrix}$, calculate the flux of $\vec{F}$ across the circle $C$ of radiu...

I am trying to find the lower- and upper-box dimensions (and show that they are the same) of the set $A=\{0,1,\frac{1}{4},\frac{1}{9},\ldots\}=\{\frac{1}{...