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Variable

  • Definition: 1. A mathematical entity that can stand for any of the members of a given set . The members of the set constitute volues of the variable, and the set itself defines the variable's range (i.e. the possible values that it may take). In considering a function f(x) of a variable x the function's value itself is also a variable. It is common to refer to the value of the function as the dependent variable and to x as the independent variable . Thus, in y = 3x + 5, y is regarded as the dependent variable and x as the independent variable. See also function; random variable. 2. An expression in logic that can stand for any element of a set (called the domain) over which it is said to range .Logical variables are in contrast to constants, which can stand only for single fixed elements. A variable is said to be free in a wff A if it is not preceded in A by a quantifier . Wffs with free variables are called open sentences, and are neither true nor false. Variables that are not free are called bound, and if all the variables in a wff are bound, then the wff is said to be closed, and is either true or false (see interpretation). For example, as the variable y in (∃x)(x is the son of y). is free, the wff is neither true nor false; but as the variables x and y are bound in (∃x)(∃y)(x is the son of y). then the wff is either true or false.

    Source: The Penguin Dictionary of Mathematics. London: Penguin, 2008. Credo Reference. Web. 07 August 2012.