If the roots of a monic polynomial are not integers, then they must have this property.
Hurwitz names a theorem which bounds the accuracy of approximations of numbers with this property, and Segre's Theorem generalizes that theorem. The signature sequences of these numbers are fractal sequences. When viewed from the origin with normal perspective along the line y = x, a quadrant of Euclid's Orchard will resemble the graph of a function continuous only at these numbers; that is   Thomae's function. If the roots of a monic polynomial are not integers, then they must have this property. For ten points, identify this property held by square roots of numbers that aren't perfect squares, and more generally by all numbers which can't be written as fractions.
Hurwitz names a theorem which bounds the accuracy of approximations of numbers with this property, and Segre's Theorem generalizes that theorem.
irrational numbers