In nonstandard analysis, a hyperinteger n is a hyperreal number that is equal to its own integer part.
An example of an infinite hyperinteger is given by the class of the sequence (1, 2, 3, ...) in the ultrapower construction of the hyperreals.
By the transfer principle of nonstandard analysis, there exists a natural extension: defined for all hyperreal x, and we say that x is a hyperinteger if
Thus, the hyperintegers are the image of the integer part function on the hyperreals.
are called, depending on the author, nonstandard, unlimited, or infinite hyperintegers.
Nonnegative hyperintegers are sometimes called hypernatural numbers.
Note that the latter gives a non-standard model of arithmetic in the sense of Skolem.