Cantor–Dedekind axiom
id:
cantor-dedekind-axiom-201-31943
title:
Cantor–Dedekind axiom
text:
In mathematical logic, the Cantor–Dedekind axiom is the thesis that the real numbers are order-isomorphic to the linear continuum of geometry. In other words, the axiom states that there is a one-to-one correspondence between real numbers and points on a line. This axiom became a theorem proved by Emil Artin in his book Geometric Algebra. More precisely, Euclidean spaces defined over the field of real numbers satisfy the axioms of Euclidean geometry, and, from the axioms of Euclidean geometry, o
brand slug:
wiki
category slug:
encyclopedia
description:
Equivalence between synthetic and analytic geometries
original url:
https://en.wikipedia.org/wiki/Cantor%E2%80%93Dedekind_axiom
date created:
date modified:
2024-03-10T23:07:44Z
main entity:
{"identifier":"Q1860722","url":"https://www.wikidata.org/entity/Q1860722"}
image:
fields total:
13
integrity:
14