Difference between revisions of "Cantor axiom"
From Encyclopedia of Mathematics
(Importing text file) |
(cf. Continuity axiom) |
||
| Line 1: | Line 1: | ||
| − | One of the axioms characterizing the completeness of the real line. It states that any nested sequence of closed intervals (that is, each interval is contained in its predecessor) with lengths tending to zero contains a unique common point. Formulated by G. Cantor, 1872. | + | One of the axioms characterizing the completeness of the real line (cf. [[Continuity axiom]]). It states that any nested sequence of closed intervals (that is, each interval is contained in its predecessor) with lengths tending to zero contains a unique common point. Formulated by G. Cantor, 1872. |
| + | |||
| + | {{TEX|done}} | ||
Latest revision as of 18:37, 15 April 2018
One of the axioms characterizing the completeness of the real line (cf. Continuity axiom). It states that any nested sequence of closed intervals (that is, each interval is contained in its predecessor) with lengths tending to zero contains a unique common point. Formulated by G. Cantor, 1872.
How to Cite This Entry:
Cantor axiom. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cantor_axiom&oldid=18914
Cantor axiom. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cantor_axiom&oldid=18914
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article