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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 or y = x.
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 T_{1} and T_{2} axioms are comparable, while the T_{1} axiom and the sobriety axiom are not).

See also comparison.

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Last updated on Thursday August 14, 2008 at 23:59:12 PDT (GMT -0700)

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Last updated on Thursday August 14, 2008 at 23:59:12 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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