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

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Sources

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