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Single Idea 13517

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

Full Idea

Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either.

Clarification

The hypothesis is that the numbers contain gaps

Gist of Idea

If set theory is consistent, we cannot refute or prove the Continuum Hypothesis

Source

report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10

Book Ref

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.273