On the Well-ordering Principle and the Principle of Finite Induction
DOI:
https://doi.org/10.31686/ijier.vol11.iss5.3922Keywords:
set of natural numbers, set of integers, Well-ordering Principle, Principle of Finite InductionAbstract
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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Accepted 2023-05-05
Published 2023-05-09
