Definition:Smaller Set/Notation

Notation for Smaller Set

Let $S$ and $T$ be sets.

$S$ 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:

$\card S \le \card T$

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 $2$
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 4$ Larger and smaller