A technique described by this adjective is often used in the proof of Zorn’s lemma, since it requires the use of a sequence also described by this adjective. For 10 points each:
[10h] Give this adjective. A technique described by this adjective is applied to omega when defining the smallest epsilon number.
ANSWER: transfinite [accept transfinite recursion or transfinite sequences]
[10e] The transfinite form of this technique can be used to avoid applying the axiom of choice in well-ordered sets. A form of proof using this technique first proves a base case, assumes the statement is true for n, and then proves it for n plus one.
ANSWER: induction [accept transfinite induction or proof by induction]
[10m] Transfinite induction is usually broken into a zero case, a limit case, and a case named for this word. The final three Peano (“pee-AH-no”) axioms concern a function with this name, which for a natural number n returns n plus one.
ANSWER: successor [accept successor function or successor operator or successor case or succ; prompt on S; reject “inductive”]
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