Property (mathematics)

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

Of operations:

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

## See also

* Unary relation

## References

1. ↑ "Introduction to Sets". https://www.mathsisfun.com/sets/sets-introduction.html.

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