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
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $3$: Cardinality: Definition $2$