Namespaces
Variants
Actions

Dedekind theorem

From Encyclopedia of Mathematics
Revision as of 17:19, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

on the continuity of the real axis

For any cut of the set of real numbers (see Dedekind cut) there exists a real number which is either the largest in the class or the smallest in the class . This statement is also known as the Dedekind principle (axiom) of continuity of the real axis (cf. Real number). The number is the least upper bound of and the greatest lower bound of .

How to Cite This Entry:
Dedekind theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dedekind_theorem&oldid=32026
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article