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nLab > Latest Changes: descending chain condition

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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeJul 12th 2023

    The entry had just a more involved definition for an object in a category, while the familiar definition for partially ordered sets was not stated explicitly. I added

    Subobjects (considered as isomorphism classes) form a possibly large partially ordered set (poset). A partially ordered set (X,≥)(X,\geq) is satisfying a descending chain condition if any inverse sequence x 1≥x 2≥x 3≥…x_1\geq x_2\geq x_3\geq\ldots eventually stabilizes, that is, there exists nn such that x n=x n+1=x n+2=…x_n = x_{n+1} =x_{n+2}=\ldots.

    diff, v6, current

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