Revision as of 10:07, 22 February 2021 edit Hellacioussatyr (talk \| contribs) Extended confirmed users 10,148 edits m →Cardinal numbers: Put def on top of the equals sign Tag: 2017 wikitext editor ← Previous edit		Revision as of 15:41, 27 August 2021 edit undo Lambiam (talk \| contribs) Autopatrolled, Extended confirmed users, Page movers 65,070 edits m →Finite sets and natural numbers: link Next edit →
Line 150: (But note that this style of definition is feasible for the ZFC numerals as well, but more circuitous: the form of the [[New Foundations\|NFU]] definition facilitates set manipulations while the form of the ZFC definition facilitates recursive definitions, but either theory supports either style of definition). The two implementations are quite different. In ZFC, choose a [[representative (mathematics)\|representative]] of each finite cardinality (the equivalence classes themselves are too large to be sets); in NFU the equivalence classes themselves are sets, and are thus an obvious choice for objects to stand in for the cardinalities. However, the arithmetic of the two theories is identical: the same abstraction is implemented by these two superficially different approaches. == Equivalence relations and partitions ==

Implementation of mathematics in set theory: Difference between revisions