more from George Cantor

Single Idea 13447

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis]

Full Idea

Cantor conjectured that there is no size between those of the naturals and the reals - called the 'continuum hypothesis'. The generalized version says that for no infinite set A is there a set larger than A but smaller than P(A).

Gist of Idea

Cantor: there is no size between naturals and reals, or between a set and its power set


report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.19

A Reaction

Thus there are gaps between infinite numbers, and the power set is the next size up from any infinity. Much discussion as ensued about whether these two can be proved.