I can't find a proper summary or reference of how to translate formulas in probability notation to arithmetic notation (i.e. when using real values)....

I actually have found the solution using double integral in polar coordinate. However, I am curious about whether I could find the same exact solution usi...

Rudin defines a power series for the exponential function and says that $E(0)=1$. But when $z=0$, the first term in the series is $0^0$, which is undefine...

What exactly is the matrix of a quadratic form? I have seen this notation occuring in a few papers (e.g. Siegel's unreadable German papers), with par...

I'm trying to solve the following question: Let $(X,d)$ be a metric space. We call a continuous function $f:X\to \mathbb R$ "good function" if for ev...

I have a question about distribution and absolute values. I was solving a problem and was wondering if it would be okay to distribute a number into an abs...

Definition: Let $M$ be a non-empty subset of $\mathbb{R}^n$ and consider $m\in\mathbb{N}$ such that $1\leqslant m\leqslant n$. M is named a regular sub ma...

If capital letters are supposed to be sets, why is $N$ used as a number? For example, in this definition of a Cauchy Sequence it says: A sequence ${p_n}$ ...

The function is $f(x) = \begin{cases} x^2\sin(1/x) & \text{if $x \neq 0$} \\ 0 & \text{if $x = 0$} \end{cases} $ I have proved that $f$ is differe...

Are there any trigonometric identity that can make $f(x) = \sin(x)+\cos(x)$ easier to plot? I have no idea how it becomes a sin graph shape in the end.