Cardinality

Cardinality is the measure of the size of a set, defined as the number of Elements in contains.

• Notation: $|A|$ denotes the cardinality of set $A$.
• For finite sets:
  • If $A=\{1,2,3\}$, then $|A|=3$.
• For infinite sets:
  • Countably infinite sets (like $\mathbb{B}$, the natural numbers) have cardinality ${\aleph }_0$.
  • Uncountably infinite sets (like $\mathbb{R}$, the real numbers) have strictly larger cardinality.