Editing Continuum hypothesis (section)

==History==

Cantor believed the continuum hypothesis to be true and for many years tried in vain to prove it.{{r|Dauben1990_1347}} It became the first on David Hilbert's [[Hilbert's problems|list of important open questions]] that was presented at the [[International Congress of Mathematicians]] in the year 1900 in Paris. [[Axiomatic set theory]] was at that point not yet formulated. 
[[Kurt Gödel]] proved in 1940 that the negation of the continuum hypothesis, i.e., the existence of a set with intermediate cardinality, could not be proved in standard set theory.{{r|Gödel1940}} The second half of the independence of the continuum hypothesis – i.e., unprovability of the nonexistence of an intermediate-sized set – was proved in 1963 by [[Paul Cohen (mathematician)|Paul Cohen]].{{r|Cohen1963}}