Property (mathematics)

For other uses, see Property (disambiguation).

In mathematical terminology, a property p defined for all elements of a set X is usually defined as a function p: X → {true, false}, that is true whenever the property holds; or equivalently, as the subset of X for which p holds; i.e. the set {x | p(x) = true}; p is its indicator function. It may be objected (see above) that this defines merely the extension of a property, and says nothing about what causes the property to hold for exactly those values.

See also

• Unary relation