First thing, the set of non integers: $\mathbb{R-Z=L}$ So could we have a parity for the numbers in set $\mathbb{L}$? I thought of it and here is my work:...

In cryptographic context, we often observe the function $\mathsf{poly}$. For example , let $n$ be an integer, this function is called in a manner such as ...

I can find proofs (but I admit I couldn't do them without referencing them) that $A_5$ is a normal subgroup of $S_5$, I also know (and the question s...

Let $f:\mathbb{R}^2 \to \mathbb{R}_+$ be the function defined piecewise by $$ f(x,y) := \begin{cases} \sqrt{1 - x^2 - y^2} &\text{, if } x^2+y^2 \leq ...

Is there any "classical" distribution that is considered bimodal? For example, "Normal" is unimodal, "Gamma" is unimodal. If I have to generate a sample o...

I was working on the question, to show that $i^i$ is a real number. That was however straight forward, $$i = e^{i\frac{\pi }{2}}$$ so $$i^i = (e^{i\frac{\...

If ${f(x) = \sqrt{x^2}}$, then f(x) can also be expressed as: C. ${|x|}$ D. $ \pm x$ I thought the answer was D, but it's C. Couldn't it be both?

I have two objects ($a$ and $b$) moving towards each other at different speeds ($30$mph and $50mph$ respectively). The distance ($d$) between them is, let...

Does the limit of $1 - \cos(x)$ as $x$ tends to zero exist? If yes, what is it? Can it be that the limit of $$ \frac{1-\cos(x)}{x} $$ as $x$ tends to zero...

I want to know how to calculate the value of sin, not using table values or calculator. I found this $\frac{(e^{ix})^2-1}{2ie^{ix}}$, but how to deal with...