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Given an ordered abelian group , let us inductively define the left action as
is an Archimedean ordered abelian group if there is a family of dependent terms
is an Archimedean ordered abelian group if there is a family of dependent terms
The integers are an Archimedean ordered abelian group.
The rational numbers are a Archimedean ordered abelian group.
Every Archimedean ordered integral domain is a Archimedean ordered abelian group.
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