Single Idea 8671

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers]

Full Idea

The set of 'real' numbers, which consists of the rational numbers and the irrational numbers together, represents "the continuum", since it is like a smooth line which has no gaps (unlike the rational numbers, which have the irrationals missing).

Gist of Idea

The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps

Source

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

The Continuum is the perfect abstract object, because a series of abstractions has arrived at a vast limit in its nature. It still has dizzying infinities contained within it, and at either end of the line. It makes you feel humble.