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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:

• 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.

See also※

• Unary relation

References※

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