On the Well-ordering Principle and the Principle of Finite Induction

Authors

DOI:

https://doi.org/10.31686/ijier.vol11.iss5.3922

Keywords:

set of natural numbers, set of integers, Well-ordering Principle, Principle of Finite Induction

Abstract

In this note the equivalence among the Well-ordering Principle, the Principle of Finite Induction and certain natural conditions concerning the set of integers is discussed, thereby clarifying facts encountered in the literature.

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References

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F. Cajori, Origin of the Name ”Mathematical Induction”, Amer. Math. Monthly 25 (1918), 197-201. DOI: https://doi.org/10.1080/00029890.1918.11998417

F.W. Lawvere, An elementary theory of the category of sets, Proc. Nat. Acad. Sci. U.S.A. 52 1964), 1506-1511. DOI: https://doi.org/10.1073/pnas.52.6.1506

F.W. Lawvere, An elementary theory of the category of sets (long version) with commentary, Reprints in Theory and Applications of Categories, No. 11 (2005),

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S. Mac Lane and Birkhoff, Algebra, Sixth Printing, Macmillan, New York, 1971.

C.P. Milies e S.P. Coelho, Nu´meros: Uma Introdu¸ca˜o `a Matema´tica. Editora da Universidade de S˜ao Paulo, S˜ao Paulo, 1998.

G. Peano, Arithmeticas principia, novo methodo exposita, Turin, 1889.

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Published

2023-05-09

How to Cite

Pombo Júnior, D. P. (2023). On the Well-ordering Principle and the Principle of Finite Induction. International Journal for Innovation Education and Research, 11(5), 42-44. https://doi.org/10.31686/ijier.vol11.iss5.3922