THE FABULOUS DESTINY OF RICHARD DEDEKIND

被引：2
|
作者：
Devillanova, Giuseppe [1 ]
Bisci, Giovanni Molica [2 ]
机构：
[1] Politecn Bari, Dipartimento Meccan Matemat & Management, Via Orabona 4, I-70126 Bari, Italy
[2] Univ Urbino Carlo Bo, Dipartimento Sci Pure & Applicate DiSPeA, Piazza Repubbl 13, I-61029 Urbino, Pesaro & Urbino, Italy
来源：
ATTI ACCADEMIA PELORITANA DEI PERICOLANTI-CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI | 2021年 / 99卷 / S1期
关键词：
INTERMEDIATE VALUE THEOREM;
D O I：
10.1478/AAPP.99S1A18
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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.
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页数：28
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