free variable
Quick Summary
In logic, a free variable is a variable whose range is not restricted by quantification. In contrast, variables that are quantified are called bound variables.123
Quantification involves attaching signs of quantity to propositions. The universal quantifier (\u2200) indicates that a formula holds for all values of a variable, while the existential quantifier (\u2203) indicates it holds for at least one value. Variables not bound by these quantifiers are considered free. For example, in the expression (\u2200\u03b5)(\u2203\u03b4) f(x) < \u03b4, \u03b5 and \u03b4 are bound variables, while f, x, and the implied constants are free.2
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