Given a free ultrafilter $U$ on the natural numbers $\mathbb{N}$, the field of hyperreal numbers $^*\mathbb{R}$
[2] can be defined as the ultrapower $\mathbb{R}^\mathbb{N}/U$
[3], which is the set of all sequences of real numbers modulo the equivalence relation $(a_n)_n \sim (b_n)_n$ if and only if $\{n \mid a_n = b_n\} \in U$.