We study about the metamathematics of Zermelo-Fraenkel set theory with
the axiom of choice. We use the validity of Addition and Multiplication. We
provide an example that the two operations Addition and Multiplication do not
commute with each other. All analyses are performed in a finite set of natural
numbers.
References
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Zermelo-Fraenkel
Set Theory—Wikipedia, the Free Encyclopedia.
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Perhaps the Best Exposition of ZFC before the Independence of AC and the
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[11]
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van Heijenoort, J. (1967) From Frege to Godel: A Source
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Zermelo, E. (1908) Untersuchungen uber die Grundlagen der Mengenlehre I. Mathematische Annalen, 65, 261-281. http://dx.doi.org/10.1007/BF01449999
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