# Property (mathematics)

## From Wikipedia, the free encyclopedia

For other uses, see Property (disambiguation).

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]}

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