In Bennett, Carbery and Wright's paper A non-linear generalisation of the Loomis–Whitney inequality and applications, Claim 5 was used to generalise the case from characteristic functions to simple functions. I figured that through direct calculations, we can obtain $$\int_U\displaystyle\prod_{j=...

I know this has been discussed before (Why is $-5^2=-25$?) but this makes no sense in my head, maybe someone can clarify. To me $-5^2$ means the number $-5$ (a number in $\mathbb R$), squared. It's not $0 - 5^2$ where $-$ is an operation. Put in other words: $x^2$ with $x=-5$ How come $-5^2$ is t...

As I write personal statements for graduate school, I want to highlight my hard work through humor and also just show my personality. As someone who works full time (in order to fund my education) as a carpenter and does research/studies in their free time while working towards a masters degree, ...