more from Michèle Friend

Single Idea 8662

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. The Infinite / h. Ordinal infinity]

Full Idea

The first 'limit ordinal' is called 'omega', which is ordinal because it is greater than other numbers, but it has no immediate predecessor. But it has successors, and after all of those we come to twice-omega, which is the next limit ordinal.

Clarification

'Ordinals' are numbers with an order

Gist of Idea

The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4)

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.13


A Reaction

This is the gateway to Cantor's paradise of infinities, which Hilbert loved and defended. Who could resist the pleasure of being totally boggled (like Aristotle) by a concept such as infinity, only to have someone draw a map of it? See 8663 for sequel.

Related Idea

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