Revision as of 04:12, 9 February 2021 edit David Eppstein (talk \| contribs) Autopatrolled, Administrators 235,616 edits Update Holmes link ← Previous edit		Revision as of 10:07, 22 February 2021 edit undo Hellacioussatyr (talk \| contribs) Extended confirmed users 10,148 edits m →Cardinal numbers: Put def on top of the equals sign Tag: 2017 wikitext editor Next edit →
Line 199: Cardinal numbers are defined in [[New Foundations\|NFU]] in a way which generalizes the definition of natural number: for any set ''A'', <math>\|A\| =_\,\overset{\mathrm{def}}{=} \left\{B \mid B \sim A\right\}</math>. In [[ZFC]], these equivalence classes are too large as usual. Scott's trick could be used (and indeed is used in [[Zermelo–Fraenkel set theory\|ZF]]), <math>\|A\|</math> is usually defined as the smallest order type (here a von Neumann ordinal) of a well-ordering of ''A'' (that every set can be well-ordered follows from

Implementation of mathematics in set theory: Difference between revisions