In mathematics, a property is any characteristic that applies to a given set.^[1] 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.^{[citation needed]}

Examples

Of objects:

• Parity is the property of an integer of whether it is even or odd

For more examples, see Category:Algebraic properties of elements.

Of operations:

• associative property
• commutative property of binary operations between real and complex numbers
• distributive property

For more examples, see Category:Properties of binary operations.