> [!NOTE] Definition 1 > Let $S$ be a [[Sets|set]]. $S$ is *countable* iff there exists a [[Bijection|bijection]] between a subset of the [[Natural Numbers|set of natural numbers]] and $S.$ > [!NOTE] Definition 2 > $S$ is countable iff it is [[Finite Set|finite]] or [[Countably Infinite Set|countably infinite set]]. > [!NOTE] Definition 3 > $S$ is countable iff there exists an [[Injection|injection]] from $S$ to $\mathbb{N}.$ # Properties