# Dictionary Definition

comparability n : qualities that are comparable;
"no comparison between the two books"; "beyond compare" [syn:
comparison, compare, equivalence]

# User Contributed Dictionary

## English

#### Translations

the condition of related objects

comparison or equivalence

- Hungarian: összehasonlíthatóság

- ttbc French: comparabilité

# Extensive Definition

In mathematics, two elements x
and y of a set partially
ordered by a relation ≤ are said to be comparable if and only
if x ≤ y or y ≤ x, or in terms of the strict version of the partial
order, if and only if x < y or y < x.http://planetmath.org/encyclopedia/PartialOrder.html
For example, two sets are comparable with respect to inclusion
if and only if one is a subset of the other.

In a classification of mathematical objects such
as topological
spaces, two criteria are said to be comparable when the objects
that obey one criterion constitute a subset (or subclass) of the
objects that obey the other one (so the T1 and T2 axioms
are comparable, while the T1 axiom and the sobriety
axiom are not).

See also comparison.