Under the continuum hypothesis, we readily see that that [tex]|{a < \aleph_1 : \textrm{a is a cardinal}}| = \aleph_0 [/tex]. What happens under the negation of CH? Is this equality still true or not? If the latter, always under the negation of CH, are there any infinite cardinals lambda for which the inequality [tex]|{a < \lambda : \textrm{a is a cardinal}}| = \lambda [/tex] fails?(adsbygoogle = window.adsbygoogle || []).push({});

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# Question about cardinality and CH

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