By using the preliminary results given in [11], we present here a concise and self contained introduction to the construction of the real field as the unique, up to increasing isomorphisms, 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.

The Fabulous Destiny of Richard Dedekind / Devillanova, G.; Molica Bisci, G.. - STAMPA. - (2020).

The Fabulous Destiny of Richard Dedekind

G. Devillanova;
2020-01-01

Abstract

By using the preliminary results given in [11], we present here a concise and self contained introduction to the construction of the real field as the unique, up to increasing isomorphisms, 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.
2020
The Fabulous Destiny of Richard Dedekind / Devillanova, G.; Molica Bisci, G.. - STAMPA. - (2020).
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/209294
Citazioni
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 2
social impact