Domain of Injection Not Larger than Codomain
From ProofWiki
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
- H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability (1996): Appendix $\text{A}.10$: Proposition $\text{A}.10.1: 1$
