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)

HeardPPBE %M %H %
714.2943%71%29%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Armand duplantis fan clubNot Just Biking10101030EMH
Belmont BWaltham A010010M
Leif Eriksen's Striking AppearanceMidnight Bus to Vista10101030EMH
Lexington ABelmont A1010020EM
Lexington BMansfield A010010M
Manchester ASheffield A0000
Waltham BMansfield B0000

Summary

TournamentEditionMatchHeardPPBE %M %H %
VAULT II at UCSB2026-03-13✓130.00100%100%100%
VAULT II Northern UK2026-04-24✓10.000%0%0%
VAULT II at Harvard2026-04-30✓410.0025%75%0%
VAULT II Stanford Online2026-07-17✓130.00100%100%100%