Definition:Count

Definition
To count a set $$S$$ is to establish a bijection between $$S$$ and a subset $\N_n$ of the natural numbers $$\N$$.

If $$S \sim \N_n$$ (where $$\sim$$ denotes set equivalence) then we have counted $$S$$ and found it has $$n$$ elements.

If $$S \sim \N$$ then $$S$$ is infinite but countable.

Also see

 * Uncountable