Single Idea 8663

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity]

Full Idea

After the multiples of omega, we can successively raise omega to powers of omega, and after that is done an infinite number of times we arrive at a new limit ordinal, which is called 'epsilon'. We have an infinite number of infinite ordinals.

Clarification

For 'omega' see Idea 8662

Gist of Idea

Raising omega to successive powers of omega reveal an infinity of infinities

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

When most people are dumbstruck by the idea of a single infinity, Cantor unleashes an infinity of infinities, which must be the highest into the stratosphere of abstract thought that any human being has ever gone.

Related Idea

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