> [!NOTE] Theorem (Cardinality of finite set is well defined) > Let $n,m\in \mathbb{N}.$ Let $S$ be a [[Finite Set|finite set]]. If there exists bijections between $S$ and $[\![n]\!]$ and $S$ and $[\![m]\!]$ : that is, $S$ has the same cardinality as $[\![n]\!]$ and as $[\![m]\!]$; then $n=m.$ **Proof**: