TITLE: Understanding "Divides" aka "|" as used logic
QUESTION [8 upvotes]: What are the rules for using the divides operator aka "$\mid$"? Is it false to say $2\mid5$ since $5/2$ = $2.5$ and $2.5\notin\mathbb{Z}$? Or does my question imply a misunderstanding?
I am seeing this for the first time in the 6.042J, Lecture 2: Induction on MIT OCW.
Thanks for the help.

REPLY [2 votes]: You're right $2|5$ is a false statement.  Here are some true statements using |, see if you can see why they are true:
$$a|b\wedge b|c\Longrightarrow a|c\\\{n|ab\Longrightarrow n|a \vee n|b\}\Longleftrightarrow \text{$n$ is prime}$$