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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Famous quotes containing the words continuum and/or hypothesis:
“The further jazz moves away from the stark blue continuum and the collective realities of Afro-American and American life, the more it moves into academic concert-hall lifelessness, which can be replicated by any middle class showing off its music lessons.”
—Imamu Amiri Baraka (b. 1934)
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