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nLab > Latest Changes: denial inequality

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  1. added table of contents, section headers, and links to apartness relation, stable equality, Kock field

    Anonymous

    diff, v7, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2022
    • (edited Dec 7th 2022)

    The half-sentence

    It is taken for granted in classical mathematics.

    needs a little addendum: What is it that is taken for granted?

    Maybe it should rather say something like this:

    In classical mathematics denial inequalities are just plain inequalities and so the notion plays no (further) role, classically.

    diff, v8, current

  3. replaced

    It is taken for granted in classical mathematics.

    with

    In classical mathematics, denial inequalities and tight apartness relations are the same, so the notion plays no further role classically.

    Anonymous

    diff, v9, current

  4. also changed

    “other inequality relations such as apartness relations”

    to

    “tight apartness relation”

    since those are the only ones which are different from denial inequalities in constructive mathematics. General apartness relations and other irreflexive symmetric relations are still relevant in other parts of mathematics, such as local rings, even in classical mathematics.

    Anonymous

    diff, v9, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2022

    Thanks!

  6. added properties of denial inequality under de Morgan’s law and under the double negation law.

    Anonymous

    diff, v10, current

1 to 6 of 6

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