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7. Varieties of Infiniteness in the Existence of Infinitely Many Primes

  • 2022
  • OriginalPaper
  • Chapter
Published in:
Author
Victor Pambuccian
Published in
Axiomatic Thinking II
Publisher
Springer International Publishing

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Abstract

The chapter delves into the various methods of proving the infinitude of prime numbers, focusing on two specific proofs: one based on the co-primality of Fermat numbers and a modified version of Euclid's proof. It applies David Hilbert's suggestion to study the essence of mathematical proofs, revealing that these proofs, while informally equivalent, are formally distinct and demonstrate different types of infinity. The chapter provides an axiomatic analysis of each proof, highlighting the necessary assumptions and the logical underpinnings that support these conclusions. This analysis shows that the two proofs are not only different but likely incompatible, offering a unique perspective on the nature of mathematical proofs and the concept of infinity.
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previous chapter Abstract Generality, Simplicity, Forgetting, and Discovery
next chapter Axiomatics as a Functional Strategy for Complex Proofs: The Case of Riemann Hypothesis
Title
Varieties of Infiniteness in the Existence of Infinitely Many Primes
Author
Victor Pambuccian
Copyright Year
2022
Book
Axiomatic Thinking II

Print ISBN: 978-3-030-77798-2

Electronic ISBN: 978-3-030-77799-9

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-030-77799-9_7
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