nLab infinite number



In a strictly weakly ordered ring RR, the natural numbers are a subset of RR, because every strictly weakly 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 weakly ordered ring RR which satisfies the archimedean property has no infinite numbers.

See also

Last revised on December 25, 2023 at 22:33:30. See the history of this page for a list of all contributions to it.