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Ideas for 'Lectures on the History of Philosophy', 'W.V. Quine' and 'Community and Association'

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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

8454	The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein]
	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.
	From: Alex Orenstein (W.V. Quine [2002], Ch.2)
	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.