Definition:Dominate (Set Theory)

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

Set $$S$$ is dominated by set $$T$$ iff there exists an injection from $$S$$ to $$T$$.

This can be written $$S \le T$$.

If $$S \le T$$ then $$T$$ dominates $$S$$ and we can write $$T \ge S$$.

Set $$S$$ is strictly dominated by set $$T$$ iff $$S \le T$$ but  $$T \not \le S$$. This can be written $$S < T$$.