Definition:Dominate (Set Theory)/Definition 2

Definition
Let $S$ and $T$ be sets.

Then $S$ is dominated by $T$ iff $S$ is equivalent to some subset of $T$.

That is, iff 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

 * Equivalence of Definitions of Dominate (Set Theory)