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]
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