## 2018-12-14

I thought about two definitions of a limit point of a set: (1) $p$ is a limit point of $S$ iff $p$ is the limit of distinct points of $S$; (2) $p$ is a limit point of $S$ iff it is an adherent point of $S\setminus \{p\}$. I tried to prove these were equivalent, and I think I succeeded. (The former definition is mentioned in Pugh’s analysis book; the latter is from Tao’s book.)

I did more problems out of Intermediate Counting & Probability. I did all of chapter 1 (review of basics) just to make sure I could do the problems.