The continuity axioms are the three of Hilbert's axioms that concern geometric equivalence. A distinct singular "continuity axiom"
is an additional axiom that must be added to those of Euclid's
Elements in order to guarantee that two equal
circles of radiusintersect each other if the
separation of their centers is less than (Dunham 1990).
Archimedes' axiom is sometimes also known as
"the continuity axiom."
intersect each other if the
separation of their centers is less than 
(Dunham 1990).
