Single Idea 8669

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility]

Full Idea

Since between any two rational numbers there is an infinite number of rational numbers, we could consider that we have infinity in three dimensions: positive numbers, negative numbers, and the 'depth' of infinite numbers between any rational numbers.

Gist of Idea

Between any two rational numbers there is an infinite number of rational numbers

Source

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

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.17


A Reaction

This is before we even reach Cantor's staggering infinities (Ideas 8662 and 8663), which presumably reside at the outer reaches of all three of these dimensions of infinity. The 'deep' infinities come from fractions with huge denominators.

Related Ideas

Idea 8662 The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend]

Idea 8663 Raising omega to successive powers of omega reveal an infinity of infinities [Friend]