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つづき
（英語版）
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Well-founded relation
(抜粋)
Other properties
If (X, <) is a well-founded relation and x is an element of X, then the descending chains starting at x are all finite, but this does not mean that their lengths are necessarily bounded.
Consider the following example: Let X be the union of the positive integers and a new element ω, which is bigger than any integer.
Then X is a well-founded set, but there are descending chains starting at ω of arbitrary great (finite) length; the chain ω, n - 1, n - 2, ..., 2, 1 has length n for any n.
The Mostowski collapse lemma implies that set membership is a universal among the extensional well-founded relations: for any set-like well-founded relation R on a class X which is extensional