Definition:Dominate (Set Theory)/Definition 2

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

• Equivalence of Definitions of Dominate (Set Theory)

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