free and bound variables

In logic and mathematics, a **free variable** is like a placeholder that isn't specifically tied to any particular thing yet—it can vary or change depending on the context. A **bound variable** is one that is restricted or fixed within a specific part of an expression, usually by a quantifier like "for all" or "there exists." Think of it like a variable inside a formula—that variable is "bound" by the quantifier, meaning its value is limited to what's specified there. Essentially, free variables are flexible and open-ended, while bound variables are confined within a defined scope.