Cardinal Number - The Continuum Hypothesis

The Continuum Hypothesis

The continuum hypothesis (CH) states that there are no cardinals strictly between and The latter cardinal number is also often denoted by ; it is the cardinality of the continuum (the set of real numbers). In this case 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).

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