Packet 13: Bonus 13
Proving this property for a function f requires setting f(a) = f(b) for an arbitrary a and b in the domain, then showing that a = b. For 10 points each:
[10e] Name this property of a function where distinct elements in the domain map to distinct elements in the codomain, such that no two different inputs produce the same output.
ANSWER: injectivity [or injective; accept one-to-one]
[10m] In set theory, this principle disproves the possibility of an injective function with a smaller codomain than domain. For 367 people, this principle guarantees that at least 2 of them share a birthday.
ANSWER: pigeonhole principle [accept Dirichlet principle or Dirichlet's Box Principle]
[10h] This theorem is equivalent to the statement that for any two sets, there exists an injective function from one to the other. This theorem states that any nonempty subset of the natural numbers has a smallest element.
ANSWER: well-ordering theorem [or well-ordering principle]
<Science - Math, Hari Ananthakrishnan> | VAULT II Packet 13 (Finals 1)
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 7 | 14.29 | 43% | 71% | 29% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Manchester A | Sheffield A | 0 | 0 | 0 | 0 |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| VAULT II at UCSB | 2026-03-13 | ✓ | 1 | 30.00 | 100% | 100% | 100% |
| VAULT II Northern UK | 2026-04-24 | ✓ | 1 | 0.00 | 0% | 0% | 0% |
| VAULT II at Harvard | 2026-04-30 | ✓ | 4 | 10.00 | 25% | 75% | 0% |
| VAULT II Stanford Online | 2026-07-17 | ✓ | 1 | 30.00 | 100% | 100% | 100% |