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nLab > Latest Changes: Archimedean ordered integral domain

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  1. Page created, but author did not leave any comments.

    Anonymous

    v1, current

  2. renaming this in line with Archimedean ordered field

    Anonymous

    diff, v6, current

  3. The statement that “Every Archimedean ordered integral domain extension of the integers is a dense linear order” is false, since ℤ\mathbb{Z} itself is an Archimedean ordered integral domain extension of the integers, but is not a dense linear order.

    What we’re really looking for is an Archimedean ordered integral domain RR with an element x∈Rx \in R and integer a∈ℤa \in \mathbb{Z} such that a<x<a+1a \lt x \lt a + 1, since that then excluded the integers.

    Anonymouse

    diff, v7, current

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