Property (mathematics)

In mathematics, a property is any characteristic that applies to a given set. Rigorously, 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. However, it may be objected that the rigorous definition defines merely the extension of a property, and says nothing about what causes the property to hold for exactly those values.

Examples
Of objects:

For more examples, see Category:Algebraic properties of elements.
 * Parity is the property of an integer of whether it is even or odd

Of operations:

For more examples, see Category:Properties of binary operations.
 * associative property
 * commutative property of binary operations between real and complex numbers
 * distributive property