FREE VARIABLES AND BOUND VARIABLES Meaning and
Definition
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Free Variables:
In the realm of formal logic and mathematics, free variables refer to symbols or variables that occur within the scope of a quantifier or logical operator without being bound by that quantifier. Essentially, a free variable is not associated with any specific value or set. It can take on any value or be assigned a value through quantification. Free variables can be found in predicate logic, where they often represent an unspecified object or element. These variables are free to change in value depending on the context or constraints defined by the logical expression or formula.
Bound Variables:
Bound variables, on the other hand, are tied to specific quantifiers or logical operators and occur within their scope. These variables are defined or “bound” by the quantifiers and can be assigned distinct values or sets. The values assigned to bound variables are restricted by the quantification or the logical expression. Bound variables are used to indicate that a particular statement holds true for some or all values within a specified domain or set. They typically act as placeholders within a logical or mathematical formula, facilitating the quantification process.
In summary, while free variables are unrestricted and can take on any value, bound variables are assigned specific values based on the quantifiers they are bound by. Both types of variables play crucial roles in formal logic, helping to express the relationships between statements, predicates, and quantification.
