dedekind::order::IsArchimedean Concept Reference

The scale axiom: Every element can be 'reached' by the Successor. FIXME: misnamed. "Every element reached by the successor" is Peano's and Dedekind's generation of the naturals from one element and a step; the Archimedean property is another axiom, that for x, y > 0 some n has n x > y [1]. Rename to the property it states, and reconcile its algebraic IsSuccessor (x + 1) with the NNO step of dedekind.category (successor, HasNNOStep), which every shipped carrier provides and IsSuccessor's carriers withhold. More...

Concept definition

template<typename T>
concept dedekind::order::IsArchimedean =  IsPartiallyOrdered<T> && IsSuccessor<T>

Detailed Description

The scale axiom: Every element can be 'reached' by the Successor. FIXME: misnamed. "Every element reached by the successor" is Peano's and Dedekind's generation of the naturals from one element and a step; the Archimedean property is another axiom, that for x, y > 0 some n has n x > y [1]. Rename to the property it states, and reconcile its algebraic IsSuccessor (x + 1) with the NNO step of dedekind.category (successor, HasNNOStep), which every shipped carrier provides and IsSuccessor's carriers withhold.