A non-zero element of an ordered field formula_1 is infinitesimal if and only if its absolute value is smaller than any element of formula_1 of the form formula_3, for formula_4 a standard natural number. Ordered fields that have infinitesimal elements are also called non-Archimedean. More generally, nonstandard analysis is any form of mathematics that relies on nonstandard models and the transfer principle. A field that satisfies the transfer principle for real numbers is a hyperreal field, and nonstandard real analysis uses these fields as "nonstandard models" of the real numbers.