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Difference between revisions of "Dedekind theorem"

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(reword, cite Dedekind (1963))
(→‎References: isbn link)
 
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====References====
 
====References====
* Richard Dedekind, "Essays on the Theory of Numbers" (tr. W.W.Beman) Dover (1963) [1901] ISBN 0-486-21010-3 {{ZBL|32.0185.01}} {{ZBL|0112.28101}}
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* Richard Dedekind, "Essays on the Theory of Numbers" (tr. W.W.Beman) Dover (1963) [1901] {{ISBN|0-486-21010-3}} {{ZBL|32.0185.01}} {{ZBL|0112.28101}}

Latest revision as of 20:44, 23 November 2023


on the continuity of the real axis; Dedekind principle, Dedekind axiom

A form of the continuity axiom for the real number system in terms of Dedekind cuts. It states that for any cut $A|B$ of the set of real numbers there exists a real number $\alpha$ which is either the largest in the class $A$ or the smallest in the class $B$. The number $\alpha$ is the least upper bound of $A$ and the greatest lower bound of $B$.


References

How to Cite This Entry:
Dedekind theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dedekind_theorem&oldid=54634
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article