set cardinality

the cardinality of a set is a measure of the number of elements of the set.

let $\text{[math]}$ be a broken link: blk:def-natural-set-inf. a set $\text{[math]}$ is said to have cardinality $\text{[math]}$ , iff it has equal cardinality with $\text{[math]}$ . we also say that $\text{[math]}$ has $\text{[math]}$ elements iff it has cardinality $\text{[math]}$ .
[cite:;taken from @tao_analysis_1 definition 3.6.5]