Definition:Smaller Set

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

$S$ is defined as being smaller than $T$ there exists a bijection from $S$ to a subset of $T$.

$S$ is smaller than $T$ can be denoted:
 * $S \le T$

Also defined as
Some sources define $S \le T$ there exists an injection from $S$ into $T$.

Also denoted as
Some sources denote this using an explicit ordering on the cardinalities of the sets in question:


 * $\card S \le \card T$

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

Also see

 * Definition:Strictly Smaller Set


 * Definition:Larger Set
 * Definition:Strictly Larger Set