Relation (mathematics) In mathematics, a relation is used to describe certain properties of things. That way, certain things may be connected in some way; this is called a relation. It is clear, that things are either related, or they are not, there are no in-betweens. Relations are classfied into four types based on mapping of elements. Formally, a relation is a set of n-tuples of equal degree. Thus a binary relation is a set of pairs, a ternary relation a set of 3-tuples, and so forth. A ternary relation however is always expressable as two binary relations. Specifically in the context of functions, this is known as currying. Other well-known relations are the Equivalence relation and the Order relation. That way, sets of things can be ordered: Take the first element of a set, it is either equal to the element looked for, or there is an order relation that can be used to classify it. That way, the whole set can be classified (compared to some arbitrarily chosen element). Relations can be transitive. One example of a transitive relation is "smaller-than". If X "is smaller than" Y, and Y is "smaller than" Z, then X "is smaller than" Z Relations can be symmetric. One example of a symmetric relation is "is equal to". If X "is equal to" Y, Y "is equal to" X. Relations can be reflexive. One example of a reflexive relation is "is equal to". X "is equal to" X. Function (mathematics) A function f takes an input x, and returns an output f(x). One metaphor describes the function as a "machine" or "black box" that for each input returns a corresponding output. The red curve is the graph of a function f in theCartesian plane, consisting of all points with coordinates of the form (x,f(x)). The property of having one output for each input is represented geometrically by the fact that each vertical line(such as the yellow line through the origin) has exactly one crossing point with the curve. In mathematics, a function[1] is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x2. The output of a function fcorresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. The input variable(s) are sometimes referred to as the argument(s) of the function. Example 1 In the relation above the domain is { 0, 3, 90 } And the range is { 1, 22, 34 } Example 2 Arrow Chart Relations are often represented using arrow charts connecting the domain and range elements.
Posted on: Sun, 29 Sep 2013 09:31:55 +0000
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