Question
In 1973, Per Enflo won a live goose for giving an example of a normed vector space with this property, but not the approximation property. For 10 points each:
[10h] Name this property, which is weaker than compactness. Banach (“BAH-nuck”) spaces possess this property of spaces in which all Cauchy (“ko-SHEE”) sequences converge.
ANSWER: completeness [accept word forms such as being complete]
[10m] In 2023, Enflo published a generalization of his solution to the invariant subspace problem to complete inner product spaces, which are named for this mathematician. This mathematician gave an example in which guests can be moved up one room infinitely many times.
ANSWER: David Hilbert (The example is Hilbert’s paradox of the Grand Hotel. When Felix Klein got the first car in Göttingen, he was not allowed to park in the spot closest to the Mathematics Institute, as that was already Hilbert’s space.)
[10e] Hilbert’s Hotel illustrates this set of integers denoted with a double-struck “N.”
ANSWER: natural numbers [or whole numbers]
<David Bass, Science - Math> ~22121~ <Editor: David Bass>
Data
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2024 PACE NSC | 06/08/2024 | Y | 36 | 15.56 | 78% | 72% | 6% |