[Home]History of Continuum hypothesis

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Revision 19 . . (edit) August 23, 2001 4:55 am by Zundark [fix link]
Revision 18 . . August 22, 2001 6:51 am by AxelBoldt [Cardinal -> Cardinal number]
Revision 17 . . (edit) August 22, 2001 4:24 am by AxelBoldt
  
Difference (from prior major revision) (minor diff, author diff)

Changed: 2c2
there is no set whose cardinality is strictly between that of the
there is no set whose cardinality is strictly between that of the

Changed: 51c51
The generalized continuum hypothesis (GCH) states that if a set's cardinality lies between that of an infinite set S and that of the power set of S, then it either has the same cardinality as the set S or the same cardinality as the power set of S: there are no in-betweens. This is a generalization of the continuum hypothesis since the continuum has the same cardinality as the power set of the integers. GCH is also independent of the set theory axioms.
The generalized continuum hypothesis (GCH) states that if a set's cardinality lies between that of an infinite set S and that of the power set of S, then it either has the same cardinality as the set S or the same cardinality as the power set of S: there are no in-betweens. This is a generalization of the continuum hypothesis since the continuum has the same cardinality as the power set of the integers. GCH is also independent of the set theory axioms.
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