Cardinality of Set of Injections/Corollary

Corollary to Cardinality of Set of Injections
Let $S$ and $T$ be sets.

Let $f: S \to T$ be a mapping.

Then $f$ cannot be an injection if:
 * $\left\vert{S}\right\vert > \left\vert{T}\right\vert$

where $\left\vert{S}\right\vert$ denotes the cardinality of $S$.

Proof
From Cardinality of Set of Injections:
 * the number of injections from $S$ to $T$, where $\left|{S}\right| > \left|{T}\right|$, is zero.

Hence the result.