nLab infinite number



In a strictly ordered ring RR, the natural numbers are a subset of RR, because every strictly ordered ring has characteristic zero. A number or element aRa \in R is an infinite number or an infinite element if for all natural numbers nn \in \mathbb{N}, n<an \lt a.

Examples of rings with infinite numbers include the hyperreal numbers and the surreal numbers.

A strictly ordered ring RR which satisfies the archimedean property has no infinite numbers.

See also

Created on December 13, 2022 at 19:07:45. See the history of this page for a list of all contributions to it.