Imagine somebody who is studying differential equations. He comes to the section on first order linear differential equations. He attempts to do the first problem in the section, but he comes up with the wrong answer. He then posts the problem and his answer to Math Stack Exchange. Somebody point...

Let $f_- (n) = \Pi_{i=0}^n ( \sin(i) - \frac{5}{4}) $ And let $ f_+(m) = \Pi_{i=0}^m ( \sin(i) + \frac{5}{4} ) $ It appears that $$\sup f_- (n) \inf f_+ (m) = \frac{5}{4} $$ Why is that so ? Update This is probably not helpful at all , but it can be shown ( not easy ) that there exist a ...

By definition, a lattice in a Lie group $G$ is a discrete subgroup $\Gamma \subset G$ such that $\Gamma \backslash G$ has finite volume. Consider now the natural projection $$ \pi : \text{SL}(n,\mathbb{R}) \to \text{PSL}(n,\mathbb{R}), $$ which is surjective with finite kernel. It is know that i...