### Single Idea 8454

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

Full Idea

The 'natural' numbers are the whole numbers 1, 2, 3 and so on. The 'rational' numbers consist of the natural numbers plus the fractions. The 'real' numbers include the others, plus numbers such a pi and root-2, which cannot be expressed as fractions.

Gist of Idea

The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc.

Source

Alex Orenstein (W.V. Quine [2002], Ch.2)

Book Reference

Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.27

A Reaction

The 'irrational' numbers involved entities such as root-minus-1. Philosophical discussions in ontology tend to focus on the existence of the real numbers.