cleispoi fu'ivla

x1 is the total-order(ing) '<' on the cardinals.

It does not assume the Axiom of Choice or the Generalized Continuum Hypothesis. See also: mrenspoi and moinspoi, with which it can be isomorphically associated under certain restrictions. Equivalent but not necessarily preferred to: cleinspoi.

In definition:

(Identical to: x1 {cleispoi}).

In notes:

x1 is the canonical total-order(ing) '<' on/of the ordinals.
x1 is the traditional/standard/classical strict total-order(ing) '<' which endows the (extended) real numbers.