Definition:Smaller Set/Definition 2

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Definition

Let $S$ and $T$ be sets.

$S$ is defined as being smaller than $T$ if and only if there exists an injection from $S$ into $T$.


Notation

$S$ is smaller than $T$ can be denoted:

$S \le T$

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

$\card S \le \card T$


Also see

  • Results about smaller set can be found here.


Sources