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

Authors
DOI:
https://doi.org/10.31686/ijier.vol11.iss5.3922
Keywords:
Array, Array, Array, Array
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.

References

G. Birkhoff and S. Mac Lane, A Survey of Modern Algebra, Eighth Printing, Macmillan, New York, 1971.

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),

-35.

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
Issue
Vol. 11 No. 5 (2023): International Journal for Innovation Education and Research
Section
Journal Articles
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Copyright (c) 2023 Dinamérico Pereira Pombo Júnior

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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