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nLab: injection

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    • CommentRowNumber1.
    • CommentAuthorroglo
    • CommentTimeSep 4th 2019
    In the page "injection", it says "strongly injective if f(x)≠f(y) whenever x≠y (which implies that the function is injective)". I would say the other way around: "injective" implies this "strongly injective" definition. So "strongly injective" should be renamed "weakly injective". Am I wrong?
    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeSep 4th 2019

    The two statements are equivalent in classical mathematics. In constructive mathematics, the statement “f(x)≠f(y)f(x)\neq f(y) whenever x≠yx\neq y” is weaker than injectivity if ≠\neq refers to the denial inequality, but stronger than injectivity if ≠\neq refers to a tight apartness relation. So the page is correct as written, since it mentions tight apartness; but it could stand to be expanded and clarified.

    • CommentRowNumber3.
    • CommentAuthorroglo
    • CommentTimeSep 5th 2019
    • (edited Sep 5th 2019)
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