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As an example, in the set of Integers, the chain -1,-2,-3,... is an infinite descending chain, but there exists no infinite chain on the Natural numbers, every chain of natural numbers has a minimal element. |
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As an example, in the set of integers, the chain -1,-2,-3,... is an infinite descending chain, but there exists no infinite chain on the natural numbers, every chain of natural numbers has a minimal element. If a partially ordered set does not contain any infinite descending chains, it is called well-founded. A total ordered set without infinite descending chains is called well-ordered. |
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