Why is $1/i$ equal to $-i$? - Mathematics Stack Exchange
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 cleaner …
Derivative of sigmoid function $\sigma (x) = \frac {1} {1+e^ {-x}}$
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
Evaluating $\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$
Sep 13, 2016 · Compute: $$\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$$ I and my friend came across this product. Is the product till infinity equal to $1$? If no, what is the answer?
factorial - Why does 0! = 1? - Mathematics Stack Exchange
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, instead of 0 ways.
Intuition for volume of a simplex being $\frac 1 {n!}$
Jul 19, 2022 · The volume of this simplex is $\frac {1} {n!}$, but I am intuitively struggling to see why. I have seen proofs for this and am convinced, but I can't help but think there must be a slicker or more …
False Proof of 1=-1 - Mathematics Stack Exchange
Aug 24, 2016 · False Proof of 1=-1 [duplicate] Ask Question Asked 9 years, 3 months ago Modified 9 years, 3 months ago
real analysis - Proof of $\lim_ {n\to \infty} \sqrt [n] {n}=1 ...
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?
Why is the determinant of a symplectic matrix 1? Ask Question Asked 13 years ago Modified 1 year, 10 months ago Viewed 15k times
The sequence of integers $1, 11, 111, 1111, \ldots$ have two elements ...
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 multiples of $2017$ …
Why the Laplace transform of the integral is 1/s?
My only suggestion would be that you should adjust your terminology a bit. The Laplace transform of the integral isn't $\frac {1} {s}$. It'd be more accurate to say The Laplace transform of an integral is equal …