Details

Autor(en) / Beteiligte

• von Neumann, John

Titel

Foundations and Elementary Properties

Ist Teil von

• Continuous Geometry, 2016, p.1-7

Ort / Verlag

Princeton: Princeton University Press

Erscheinungsjahr

2016

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The basis of our discussion is a classLof elements$a,b,c,\cdots$, two or more in number, together with a binary relation < between pairs of elements ofL. Unless otherwise specified, Axioms I—VI listed below will be assumed. Axiom I: Order. I1:a<afor no elementa. I2:a<b<cimpliesa<c. Definition 1.1:a>bmeansb<a;a≦bmeansa<bora=b;a≧bmeansb≦a. Axiom II. Continuity. II1: For every setS⊂L, there is an elementΣ(S) inL, which is aleast upper boundofS, i.e.