Bonus
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”]
<Other Science>
Answerlines and category may not exactly match the version played at all sites
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Stanford | Chicago A | 10 | 10 | 10 | 30 | HEM |
| Toronto A | Illinois A | 0 | 10 | 10 | 20 | EM |
| Waterloo A | Georgia Tech | 10 | 10 | 10 | 30 | HEM |
Summary
| Tournament | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|
| 2025 ACF Nationals | Yes | 3 | 26.67 | 100% | 100% | 67% |