May 11, 2015 · 11 There are multiple ways of writing out a given complex number, or a number in general. Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot …

In my AI textbook there is this paragraph, without any explanation. The sigmoid function is defined as follows $$\sigma (x) = \frac {1} {1+e^ {-x}}.$$ This function is easy to differentiate

Intending on marking as accepted, because I'm no mathematician and this response makes sense to a commoner. However, I'm still curious why there is 1 way to permute 0 things, …

Thomson et al. provide a proof that $\lim_ {n\rightarrow \infty} \sqrt [n] {n}=1$ in this book (page 73). It has to do with using an inequality that relies on the binomial theorem: I have an alternat...

Why is the determinant of a symplectic matrix 1? Ask Question Asked 13 years ago Modified 1 year, 10 months ago Viewed 15k times

May 9, 2016 · Prove that the sequence $\ {1, 11, 111, 1111, .\ldots\}$ will contain two numbers whose difference is a multiple of $2017$. I have been computing some of the immediate …

Mar 20, 2015 · What you are fundamentally saying is that if you have a tree with n vertex and n-1 edges, you can obtain a tree with n+1 vertices and n edges. You can add the new edge to any …

Feb 1, 2012 · I need to prove that there are infinitely many primes of the form $4k+1$. I have proved that $-1$ is not a quadratic residue modulo $4k-1$ and is a quadratic residue modulo …

Jan 15, 2017 · Hope this image helps (pythagorean identity?): And as to the $\pm$, it simply because $\cos (\arcsin (x))$ is only equal to one value, and this value can be only $+$ or $-$, …

Jan 28, 2018 · The inverse of $ (X^TX)^ {-1}$ is of course $X^TX$. I suspect that's not what you actually meant, though.