Question
Infinite descent involves contradicting this theorem by showing that a falsehood would have to apply to arbitrarily many smaller numbers. For 10 points each:
[10h] Name this theorem that is often conflated with the less general statement that every nonempty subset of N contains a least element.
ANSWER: well-ordering theorem [accept well-ordering principle]
[10e] N denotes this set, which can be defined as either the set of non-negative integers or of positive integers.
ANSWER: natural numbers [or whole numbers; prompt on counting numbers by asking “what is the more formal name?”]
[10m] Work on the well-ordering theorem caused Ernst Zermelo to introduce this equivalent statement. This statement, which is the "C" in "ZFC," enables the creation of a set consisting of one element from each of infinitely many collections.
ANSWER: axiom of choice [prompt on AC]
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