The Archimedean property states that every positive element in a strictly ordered cancellative commutative monoid is bounded above by a natural number.
So an object satisfying the Archimedean property has no infinite elements. If the strict order is additionally a connected relation and thus a linear order, every infinitesimal element is equal to zero.
Let be the set of positive integers.
Let be a strictly ordered cancellative commutative monoid. The positive integers are embedded into the function monoid ; there is an injection such that and for all .
The archimedean property states that for every such that and , then there exist such that .
By uncurrying one gets an action such that and for all and . The archimedean property then states that for all such that and , there exist such that .
Created on January 9, 2023 at 00:50:55. See the history of this page for a list of all contributions to it.