Definition:Almost All/Set Theory/Uncountable

Definition
Let $S$ be an uncountably infinite set.

Let $P: S \to \left\{ {\text{true}, \text{false} }\right\}$ be a property of $S$ such that:
 * $\left\{ {s \in S: \neg P \left({s}\right)}\right\}$

is countable (either finite or countably infinite).

Then $P$ holds for almost all of the elements of $S$.