His continuum hypothesis is the proposition that ???? is the same as ℵ1. This hypothesis has been found to be independent of the standard axioms of mathematical set theory; it can neither be proved nor disproved from the standard assumptions.
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Anonymous2013-08-31 20:32
The continuum hypothesis (CH) states that there are no cardinals strictly between ℵ0 and 2ℵ0. The latter cardinal number is also often denoted by ????; it is the cardinality of the continuum (the set of real numbers). In this case 2ℵ0 = ℵ1. The generalized continuum hypothesis (GCH) states that for every infinite set X, there are no cardinals strictly between | X | and 2| X |. The continuum hypothesis is independent of the usual axioms of set theory, the Zermelo-Fraenkel axioms together with the axiom of choice (ZFC).