# 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:

$\card S > \card T$

where $\card S$ denotes the cardinality of $S$.

## Proof

the number of injections from $S$ to $T$, where $\card S > \card T$, is zero.

Hence the result.

$\blacksquare$