nLab archimedean group

Contents

Contents

Definition

An archimedean group is a linearly ordered group which satisfies the Archimedean property, in which every positive element is bounded above by a natural number.

So an archimedean group has no infinite elements (and thus no non-zero infinitesimal elements).

Properties

Examples

Archimedean groups include

Non-archimedean groups include

See also

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