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.

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.