Definition:Dominate (Set Theory)/Definition 2
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Definition
Let $S$ and $T$ be sets.
Then $S$ is dominated by $T$ if and only if $S$ is equivalent to some subset of $T$.
That is, if and only if there exists a bijection $f: S \to T'$ for some $T' \subseteq T$.
The notation $S \preccurlyeq T$ is used to indicate that $S$ dominates $T$.
Also see
Sources
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 4$: Number systems $\text{I}$: A set-theoretic approach