Beatty's Theorem applies to a pair of numbers of this type. They form a set of measure one in the interval (0,1), and their indicator function can therefore be Lebesgue integrated, but not Riemann integrated over this interval, as illustrated by a function which is continuous only on these named for Dirichlet.
Beatty's Theorem applies to a pair of numbers of this type. They form a set of measure one in the interval (0,1), and their indicator function can therefore be Lebesgue integrated, but not Riemann integrated over this interval, as illustrated by a function which is continuous only on these named for Dirichlet. They can be generated from another set of numbers by employing Dedekind cuts. The square root of any integer that is not a perfect square is, FTP, one of what class of real numbers that cannot be expressed as the quotient of two integers, such as pi and e?
Beatty's Theorem applies to a pair of numbers of this type. They form a set of measure one in the interval (0,1), and their indicator function can therefore be Lebesgue integrated, but not Riemann integrated over this interval, as illustrated by a function which is continuous only on these named for Dirichlet.
{irrational} numbers