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nLab > Latest Changes: Euclidean field

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    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 8th 2022
    • (edited May 8th 2022)

    changed “An Euclidean field…” to “A Euclidean field…”

    hyperlinked functional equation and real numbers

    removed the superfluous duplicate of the word “Wikipedia”

    added plural redirect [[!redirects Euclidean fields]]

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 8th 2022

    Changed “…for all real numbers x∈ℝx\in \mathbb{R}” to refer to all elements of the given field instead, since eg the real algebraic numbers are an example, as are even smaller fields.

    Added two nontrivial examples: the real algebraic numbers and the constructible numbers

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 8th 2022

    Clarifying notation, and also a nod to the constructive viewpoint.

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 8th 2022

    It’s somewhat confusingly worded. I think “partial function” here refers to a partial function F→FF \to F whose domain is [0,∞)[0, \infty) (so a total function viewed as [0,∞)→F[0, \infty) \to F). Could someone confirm or deny?

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 9th 2022

    I think that’s what it’s meant to be.

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