[citation needed] An open formula does not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like true or false.
For example, when reasoning about natural numbers, the formula "x+2 > y" is open, since it contains the free variables x and y.
In contrast, the formula "∃y ∀x: x+2 > y" is closed, and has truth value true.
Open formulas are often used in rigorous mathematical definitions of properties, like (with free variables x, y, and bound variable z) defining the notion of "aunt" in terms of "parent" and "sister".
The attachment of the predicate letter P (is prime) to each number from the Fermat sequence gives a set of closed formulae.