Definition:Strictly Smaller Set

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

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


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


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

$S$ is strictly smaller than $T$ can be denoted:
 * $S < T$

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

Also see

 * Definition:Smaller Set


 * Definition:Strictly Larger Set
 * Definition:Larger Set