<logic> There is no cardinal, a, such that aleph0 < a < c, where c is the cardinality of the continuum. Proving or disproving the continuum hypothesis was the first problem on Hilbert's famous list of problems in 1900. Goedel (1938) and Cohen (1963) have proved that it is neither provable nor disprovable from standard set theory. Usually abbreviated to CH.
Generalized continuum hypothesis
For every transfinite cardinal, a, there is no cardinal b such that a < b2^a. Usually abbreviated to GCH.
[Glossary of First-Order Logic]
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<logic> The numerical continuum is the series of real numbers; the linear continuum is the series of points on a geometrical line.
[Glossary of First-Order Logic]
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