My question is related with the definition of Cauchy sequence As we know that a sequence $(x_n)$ of real numbers is called Cauchy, if for every positive r...

I've read Wikipedia about it and it says: In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between see...

Am I the only one to find these alternative names stupid? one-to-one = injective one-to-one correspondance = bijective onto = surjective Why don't th...

Show that $x^{2} \equiv 1 \pmod{15}$ has four incongruent solutions mod 15. My instinct was to find the primitive root and then use a theorem to directly ...

How do I transform the integral $$\int_0^\infty e^{-x^2} dx$$ from 0 to $\infty$ to o to 1 and. I have to devise a monte carlo algorithm to solve this fur...

Consider the following decision problem: given two lists of positive integers $a_1, a_2, \dots, a_n$ and $b_1, b_2, \dots, b_m$ the task is to decide if $...

Consider the integral $$\int \sec^4(x)\tan(x)$$ Now right off the bat I see two ways of solving this. Let u=$\sec(x)$ 2.Use integration by parts Now doing...

I have the linear program $$\begin{array}{ll} \text{minimize} & -2x-5y\\ \text{subject to} & 3x + 4y \geq 5\\ & x, y \geq 0\end{array}$$ I can...

I am learning how to calculate convolution of basic signals, such as rectangular ones. Specifically, the definition of such a signal is: $$ \operatorname{...

Working on the book: Derek Goldrei. "Propositional and Predicate Calculus" (p. 40) The author briefly introduces the concept of a function v: We...