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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.
In mathematics, the associative property [1] is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
Today the commutative property is a well-known and basic property used in most branches of mathematics. The first recorded use of the term commutative was in a memoir by François Servois in 1814, [1] [10] which used the word commutatives when describing functions that have what is now called the commutative property.
In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality ...
In probability, a generic property is an event that occurs almost surely, meaning that it occurs with probability 1. For example, the law of large numbers states that the sample mean converges almost surely to the population mean. This is the definition in the measure theory case specialized to a probability space.
In mathematics, a mathematical object is said to satisfy a property locally, if the property is satisfied on some limited, immediate portions of the object (e.g., on some sufficiently small or arbitrarily small neighborhoods of points).
The manipulations of the Rubik's Cube form the Rubik's Cube group.. In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.
There is a corresponding greatest-lower-bound property; an ordered set possesses the greatest-lower-bound property if and only if it also possesses the least-upper-bound property; the least-upper-bound of the set of lower bounds of a set is the greatest-lower-bound, and the greatest-lower-bound of the set of upper bounds of a set is the least ...