Document (#43350)

Author
Felgner, U.
Title
¬Die Begriffe der Äquivalenz, der Gleichheit und der Identität
Source
Jahresbericht der Deutschen Mathematiker-Vereinigung. 122(2020) H.2, S.109-129
Year
2020
Series
Survey article
Abstract
"Der Begriff der Gleichheit ist uns Mathematikern vielleicht der geläufigste; dennoch läßt sich schwer sagen, was wir unter ihm verstehen." - Mit diesem Satz beginnt GERHARD HESSENBERG sein Buch über die .Grundlagen der Geometrie' ([24], Berlin, 1930, §1). Er kommt nach einer ausführlichen Diskussion zum Schluß, daß die Relation der Gleichheit nichts anderes als eine Äquivalenzrelation sei, also eine symmetrische, transitive und reflexive Relation, und daß auch umgekehrt jede symmetrische, transitive und reflexive Relation eine Gleichheitsbeziehung sei. Die Begriffe Gleichheit und Äquivalenz wären demnach synonym. Schaut man im .Mathematischen Wörterbuch' von J. NAAS & H.L. SCHMID (Berlin, 1967) nach, so findet man unter dem Stichwort Gleichheit (p. 639) genau dieselbe Definition: "Die Gleichheit ist eine Äquivalenzrelation und umgekehrt kann jede Äquivalenzrelation als eine besondere Art von Gleichheit aufgefaßt werden."
Content
Vgl. die Ergänzung zur Verfügbarkeit unter Open access unter: Jahresbericht der Deutschen Mathematiker-Vereinigung. 123(2021) H.3, S.217-218. DOI: https://doi.org/10.1365/s13291-020-00214-0.
Theme
Begriffstheorie
Field
Mathematik

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