more from George Cantor

### Single Idea 15906

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

Full Idea

Cantor said he could show that every infinite set of points on the line could be placed into one-to-one correspondence with either the natural numbers or the real numbers - with no intermediate possibilies (the Continuum hypothesis). His proof failed.

Gist of Idea

Cantor tried to prove points on a line matched naturals or reals - but nothing in between

Source

report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.1

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.43