# Domain of Injection Not Larger than Codomain

## Theorem

Let $f: S \rightarrowtail T$ be an injection.

Then:

- $\left|{S}\right| \le \left|{T}\right|$

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

## Proof

## Sources

- 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*: Appendix $\text{A}.10$: Proposition $\text{A}.10.1: 1$