Bonus
Quillen’s “small object” argument uses a variant of this procedure to construct a factorization of morphisms into two terms. For 10 points each:
[10h] Name this procedure that requires a well-ordered set and the axiom of choice. This procedure involves verifying a “successor case” and a “limit case” to show that a property “P of alpha” is true for all alpha.
ANSWER: transfinite induction [accept transfinite recursion; prompt on induction or recursion]
[10m] Gerhard Gentzen used transfinite induction up to a particular ordinal in his consistency proof for this set of statements. An Italian mathematician names these statements that define the natural numbers.
ANSWER: Peano axioms [or Peano postulates; or Dedekind–Peano axioms; or Dedekind–Peano postulates; accept “Peano’s” in place of “Peano”]
[10e] Transfinite recursion can be used to construct a “universe” of well-founded sets named for this polymath. This Hungarian-born “father of game theory” wrote Mathematical Foundations of Quantum Mechanics.
ANSWER: John von Neumann [or Neumann János]
<Ohio State B, Other Science>
| Editions | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|
| 1 | 40 | 13.00 | 58% | 63% | 10% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Columbia B | Maryland B | 0 | 10 | 0 | 10 | M |
| Columbia C | Rutgers A | 0 | 10 | 0 | 10 | M |
| George Washington B | Haverford B | 0 | 0 | 0 | 0 | |
| Johns Hopkins A | Haverford A | 0 | 10 | 0 | 10 | M |
| NYU A | Penn B | 0 | 10 | 10 | 20 | ME |
| Penn A | Maryland A | 0 | 10 | 10 | 20 | ME |
| Vassar A | NYU B | 0 | 0 | 10 | 10 | E |
| Yale A | Cornell B | 0 | 10 | 10 | 20 | ME |
Summary
| Tournament | Edition | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|
| Lower Mid-Atlantic | 2025-02-01 | 6 | 6.67 | 33% | 33% | 0% |
| Midwest | 2025-02-01 | 6 | 13.33 | 67% | 50% | 17% |
| Northeast | 2025-02-01 | 4 | 17.50 | 50% | 75% | 50% |
| Overflow | 2025-02-01 | 4 | 15.00 | 75% | 75% | 0% |
| Pacific Northwest | 2025-02-01 | 2 | 15.00 | 50% | 100% | 0% |
| UK | 2025-02-01 | 10 | 14.00 | 70% | 60% | 10% |
| Upper Mid-Atlantic | 2025-02-01 | 8 | 12.50 | 50% | 75% | 0% |