hyperinteger

In nonstandard analysis, a hyperinteger n is a hyperreal number that is equal to its own integer part. A hyperinteger may be either finite or infinite. A finite hyperinteger is an ordinary integer. An example of an infinite hyperinteger is given by the class of the sequence in the ultrapower construction of the hyperreals.

==Discussion== The standard integer part function: \lfloor x \rfloor is defined for all real x and equals the greatest integer not exceeding x. By the transfer principle of nonstandard analysis, there exists a natural extension: {}^*\! \lfloor \,\cdot\, \rfloor defined for all hyperreal x, and we say that x is a hyperinteger if x = {}^*\! \lfloor x \rfloor. Thus, the hyperintegers are the image of the integer part function on the hyperreals.