more from Michèle Friend

Single Idea 8670

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number]

Full Idea

A number is 'irrational' just in case it cannot be represented as a fraction. An irrational number has an infinite non-repeating decimal expansion. Famous examples are pi and e.

Gist of Idea

A number is 'irrational' if it cannot be represented as a fraction


Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5)

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.19

A Reaction

There must be an infinite number of irrational numbers. You could, for example, take the expansion of pi, and change just one digit to produce a new irrational number, and pi has an infinity of digits to tinker with.