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The question is motivated by the following multiple-choice problem: If $R$ is a ring with the property that $r=r^2$ for each $r\in R$, which of the follow...
State the number of positive integers in the range of 1 to 'x' which are perfect squares or cubes or perfect fourth powers of an integer. My try...
In every textbook or online paper I read, the proof of continuity of probability measure starts by assuming a monotone sequence of sets $(A_n)$. Or it ass...
My question is about using "decrease by" without any ambiguity. I'm reading a paper where the authors consider a set $X$ defined respectively to a tr...
I could find this in Wikipedia Component: A connected component of a graph is a maximal connected subgraph. The term is also used for maximal subgraphs or...
I have a strong background in mathematics, in particular, in real analysis, functional analysis and topology. But, recently, i have became interested in s...
For example, let $ r_i \sim \operatorname{Binomial} (n, p_i)$, where $i \in [1,m]$. Assume that $ r_i $ are independent and also, put an inequality, $ p_1...
In 1995 the Connect-4 Game was solved with a brute force approach. Using the standard 6 high / 7 wide grid, first player can force a win in 41 moves. Comp...
Prove that $2\sin^{-1}\sqrt x - \sin^{-1}(2x-1) = \dfrac\pi2$. Do you integrate or differentiate to prove this equality? If so, why?
In the set $\mathbb{C}$ of complex numbers, the minus sign "-" may be used for following: As a unary operator $-_u$, given a complex number $a$, $-_ua$ is...
