For 10 points, name these real numbers not expressible as a quotient of two integers.
A spectrum sequence with one of these numbers as a base is called a Beatty sequence. The Minkowski question mark function maps them to another set of numbers. Quadratic ones can be written as periodic continued fractions. They can be produced by a Dedekind cut. All square roots of square-free numbers are these numbers, a subset of which is the transcendental numbers. Their decimal representations do not terminate or repeat. Examples include pi, e, and the square root of two. For 10 points, name these real numbers not expressible as a quotient of two integers.
A spectrum sequence with one of these numbers as a base is called a Beatty sequence.
{irrational} numbers [prompt on {quadratic surds} or {quadratic irrationals}]