Definition:Dominate

[edit] Set Theory

Let $S$ and $T$ be sets.

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

This can be written:

Sources differ.

If $S \preccurlyeq T$ then $T$ dominates $S$ and we can write $T \succcurlyeq S$ .

Set $S$ is strictly dominated by set $T$ iff $S \preccurlyeq T$ but $T \not \preccurlyeq S$ .

This can be written $S \prec T$ or $S < T$ .

Then $\left \langle {a_n} \right \rangle$ dominates $\left \langle {z_n} \right \rangle$ iff:

$\forall n \in \N: \left|{z_n}\right| \le a_n$