Search results
Results from the WOW.Com Content Network
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.
The typical diagram of the definition of a universal morphism. In mathematics, more specifically in category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions. Thus, universal properties can be used for defining some objects independently from the method chosen for constructing them.
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, 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 least-upper-bound property is an example of the aforementioned completeness properties which is typical for the set of real numbers. This property is sometimes called Dedekind completeness . If an ordered set S {\displaystyle S} has the property that every nonempty subset of S {\displaystyle S} having an upper bound also has a least upper ...
In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality ...
In mathematics, the associative property [1] is a property of some binary operations 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 .
In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c.. Every partial order and every equivalence relation is transitive.