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In psychology, philosophy, and logic, a property is an attribute of an object; thus a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. Properties are therefore subject to the Russell's paradox/Grelling-Nelson paradox. It differs from the logical concept of class by not having any concept of extensionality, and from the philosophical concept of class in that a property is considered to be distinct from the objects which possess it.
In mathematical terminology, given any element of a set X, a certain property p is either true or false. Formally, a property p: X → {true, false}. Any property gives rise in a natural way to the set {x: x has the property p} and the corresponding indicator function.
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