Real closed field

element of a nonstandard model of the reals, which can be infinite or infinitesimal

a totally ordered proper class containing the real numbers as well as hyperreal numbers such as infinity and infinitesimals.

alternative formulation of calculus using a logically rigorous notion of infinitesimal numbers

class of extensions of the real numbers

Non algebraically closed field whose extension by sqrt(–1) is algebraically closed

system of numbers with non-finite quantities

In non-standard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers.