Definition:Dominate (Set Theory)/Definition 2

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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