Examples of these kinds of numbers include e, the square root of two, and pi.
Numbers from this set are multiplied to generate Beatty sequences, and Apéry's theorem states that the sum as n goes from one to infinity of one over n cubed is one of these numbers. The reals can be constructed by exploiting the fact that this set's complement lacks the least upper bound property; that procedure is known as creating Dedekind (DEH-duh-kend) cuts. A classic proof for the existence of this set constructs an example by considering the equation x squared equals two y squared, deriving a contradiction because y must be both odd and even. Examples of these kinds of numbers include e, the square root of two, and pi. Give the name of this set of numbers that cannot be written as a simple fraction of two integers.
Numbers from this set are multiplied to generate Beatty sequences, and Apéry's theorem states that the sum as n goes from one to infinity of one over n cubed is one of these numbers.
{irrational} numbers [accept {J}]