On the Fundamental Theorem of Arithmetic and Euclid's Theorem

Hendra Gunawan
715 219

Abstract


We encounter a circular argument in the proofs of Euclid’s theorem on
the infinitude of primes that rely on the Fundamental Theorem of Arithmetic. We discover this by carefully observing the set of primes involved in the statement.

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References


M. Aigner and G.M. Ziegler, Proofs from THE BOOK, Springer (2014)

C.F. Gauss, Disquisitiones Arithmaticae, Leipzig (1801) [English translation by A.C.

Clarke, Yale Univ. Press (1966)]

S. Mac Lane and G. Birkhoff, Algebra, American Mathematical Society (1999)

L.J. Rips, “Circular reasoning”, Cognitive Science 26 (2002), 767–795

D. Varberg, E. Purcell, and S. Rigdon, Calculus, 9th ed., Pearson International Edition

(2006)