Cantor's Axiom

Cantor's axiom

[′kan·tərz ′ak·sē·əm]

(mathematics)

The postulate that there exists a one-to-one correspondence between the points of a line extending indefinitely in both directions and the set of real numbers.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Cantor’s Axiom

 

one of the axioms characterizing the continuity of a line. It states that a nested sequence of closed intervals whose lengths tend to zero has a single common point. It was formulated by G. Cantor in 1872.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.