Understanding "Divides" aka "|" as used logic 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.

$n\mid m$ means that $n$ divides $m$; $2\mid5$ is false since it leaves a remainder of $1$, thus $2\nmid5$. ($x\nmid y$ stands for that $x$ does not divide $y$)
More examples:  
$2\mid6$ since remainder when $6$ is divided by $2$ is zero.
$3\mid 9^n+27n, \forall n\in\mathbb{N}$ (which means that forall $n$ that's a natural number)
