The fabulous destiny of Richard Dedekind

Authors

  • Giuseppe Devillanova Politecnico di Bari
  • Giovanni Molica Bisci Università degli Studi di Urbino Carlo Bo

DOI:

https://doi.org/10.1478/AAPP.99S1A18

Abstract

By using the preliminary results given in a previous divulgative note, we present here a concise and self–contained introduction to the construction of the real field as the unique, up to increasing isomorphism, Dedekind complete totally ordered field. Moreover, we also show the equivalence between the Dedekind completeness property on totally ordered fields and some meaningful well–known notions present in the literature, such as the Cauchy completeness on totally ordered Archimedean fields. This characterization result allows us to correctly encode the Dedekind completeness for totally ordered fields in the general abstract setting of metric spaces. We believe that the essential parts of the paper can be easily accessed by anyone with some experience in abstract mathematical thinking. The paper completes the lecture given by the second author during the International Workshop on New Horizons in Teaching Science in Messina on June 2018.

Author Biographies

  • Giuseppe Devillanova, Politecnico di Bari
    Dipartimento di Meccanica, Matematica e Management,Via Orabona, 4, 70126 Bari
  • Giovanni Molica Bisci, Università degli Studi di Urbino Carlo Bo
    Dipartimento di Scienze Pure e Applicate (DiSPeA), Piazza della Repubblica 13, 61029 Urbino (Pesaro e Urbino)

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Published

2021-09-30

Issue

Vol 99, SUPPL NO 1 (2021): New Horizons in Teaching Science 2019

Section

New Horizons in Teaching Science (Conference Proceedings)

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