more from George Cantor

### Single Idea 10112

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities]

Full Idea

Cantor showed that the complete totality of natural numbers cannot be mapped 1-1 onto the complete totality of the real numbers - so there are different sizes of infinity.

Gist of Idea

The naturals won't map onto the reals, so there are different sizes of infinity

Source

report of George Cantor (works [1880]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.4

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.99