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nLab > Latest Changes: real square root function

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

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 8th 2022

    It’s not clear to me that its useful to have this as an entry separate from square root.

    I think if you want the content of this entry to be find-able by readers, there should at least be more than a bare link from square root to it (at least a comment like: “For more discussion of … the reader may go to a dedicated entry real square root”).

  3. It is not exactly clear that a principal square root function. defined on [0,∞)[0, \infty) by the functional equation x 2=|x|\sqrt{x^2} = \vert x \vert as stated in the article, exists in a given set of real numbers in constructive mathematics.

    As a result, I’ve asked for a proof of the existence of a principal square root function in a Cauchy complete Archimedean ordered field on this MathOverflow thread, and François G. Dorais provided a constructive real analytic proof of the existence of the principal square root function defined on [0,∞)[0, \infty).

    When I have the time, I’ll try to copy the proof over to the nlab, and credit Dorais appropriately, or if somebody else wants to do it before I do, they could go do it as well.

  4. same person who ported Mark Saving’s proof onto the field article the other day, I have now ported the proof on the MathOverflow page over to this article and made it into a definition of the principal square root.

    Anonymous

    diff, v4, current

  5. this article seems to be about the square root function on the real numbers

    Anonymous

    diff, v4, current

  6. Adding publication information and doi for the Fred Richman reference:

    Anonymouse

    diff, v10, current

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