Definition:Strictly Larger Set

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

$S$ is defined as being strictly larger than $T$ :


 * $(1): \quad$ There exists a bijection from $T$ to a subset of $S$


 * $(2): \quad$ There exists no such bijection from $S$ to a subset of $T$.

$S$ is strictly larger than $T$ can be denoted:
 * $S > T$

Also known as
If $S$ is strictly larger than $T$, then $S$ is said to be of strictly higher cardinality than $T$.

Also see

 * Definition:Larger Set


 * Definition:Strictly Smaller Set
 * Definition:Smaller Set