Question
The Cantor-Schroeder-Bernstein theorem was first proven by George Cantor using this result. For 10 points each:
[10m] Name this result often attached to Zermelo-Fraenkel set theory. This axiom, equivalent to Tychonoff’s theorem, allows one to pick an element from each of a collection of non-empty sets.
ANSWER: axiom of choice
[10h] The axiom of choice is equivalent to an axiom named for this property of sets. By definition, every non-empty subset of a set with this property has a least element.
ANSWER: well-ordered [accept well-ordering axiom]
[10e] The axiom of choice equivalently states that the Cartesian variety of this operation on a collection of non-empty sets is non-empty. The “dot” and “cross” variety of this operation are often used in vector calculus.
ANSWER: products
<AG, Other Science>
Summary
| 2023 ILLIAC (Cornell) | 2023-10-21 | Y | 4 | 27.50 | 100% | 100% | 75% |
| 2023 ILLIAC (Mainsite) | 2023-10-21 | Y | 8 | 20.00 | 88% | 63% | 50% |
Data
| Cornell Wind | RIT | 10 | 0 | 10 | 20 |
| Rochester A | Cornell Fire | 10 | 10 | 10 | 30 |
| Cornell Earth | Rochester C | 10 | 10 | 10 | 30 |
| Columbia Ly-α | Rochester B | 10 | 10 | 10 | 30 |