New posts in Proof Verification

Showing that a dense subspace $Y$ of a first countable separable topological space is separable

I don't understand the explanation of Proof by Contradiction

Show that for any subset $S \subset V$ that the span(S) is the smallest subspace of $V$ containing $S$.

Student claims $\lim_{x \to 0^+} \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} = \lim_{h \to 0} \lim_{x \to 0^+} \frac{f(x+h)-f(x)}{h}$. Is it justified?

No. of finite group (nonidentity)elements $x$ satisfying $x^5=e$ is a multiple of $4$

Gelfand-Kolmogorov Theorem for the space $C(X)$ with compact $X$: ring vs algebra version.

Prove that $(\mathbf{AB})^{T} = \mathbf B^{T}\mathbf A^{T}$ where $\mathbf A$ and $\mathbf B$ are matrices

Prove that $e$ is irrational

To prove that $(n-1)!+1$ is not a power of $n$.

For quartic $f(x)$, why can't the number of distinct real solutions of $f(x)=1$, $f(x)=2$, $f(x)=3$, $f(x)=4$ be $1$, $3$, $2$, $4$, respectively?