One type of these can be approximated by solving Pell's equations, and examples of these with periodic continued fractions are their quadratic types. This set can be constructed from its complement by using Dedekind cuts. Hip
One type of these can be approximated by solving Pell's equations, and examples of these with periodic continued fractions are their quadratic types. This set can be constructed from its complement by using Dedekind cuts. Hippasus arrived at a contradiction in the parity of (*) square numbers to find these numbers, and Cantor's diagonal argument proved that almost all real numbers are these numbers which have non-terminating and non-repeating decimal representations. For ten points, identify these numbers that cannot be expressed as a fraction of two integers "a over b," exemplified by e and the square root of two.
One type of these can be approximated by solving Pell's equations, and examples of these with periodic continued fractions are their quadratic types.
irrational numbers [accept square roots before "quadratic"]