Question
The countability of this set can be proven by identifying it with a proper subset of integer lattice points in the coordinate plane. For 10 points each:
[10e] Name this set denoted Q that contains all fractions of integers.
ANSWER: rational numbers
[10h] Because the rationals are countable and the reals are not, the rationals have this property, which means their complement occurs “almost everywhere.” A function is Riemann integrable if it is discontinuous only on a subset with this property.
ANSWER: Lebesgue (“luh-BEG”) measure zero
[10m] The rationals are also dense in the reals, which means that the reals are the smallest set with this property that contains the rationals. The smallest superset of a set S with this property is the union of S with all its limit points.
ANSWER: closed [accept closure]
<Other Science>
Summary
| 2023 ACF Winter @ Columbia | 11/11/2023 | Y | 5 | 10.00 | 80% | 20% | 0% |
Data
| NYU A | Columbia A | 10 | 0 | 0 | 10 |
| Columbia B | Yale A | 0 | 0 | 0 | 0 |
| Rutgers A | Cornell C | 10 | 0 | 0 | 10 |
| Haverford | Yale B | 10 | 0 | 0 | 10 |
| Penn A | Princeton A | 10 | 0 | 10 | 20 |