n. 1. a number that is greater than all the numbers in a given set of numbers (an upper bound), or less than all the numbers in a given set (a lower bound). If the bound holds uniformly, usually for every member of a sequence, it is a uniform bound. See supremum, infimum. 2. more generally, an element of an ordering that has the same ordering relation to all the members of a given subset; for example, since it is a subset of every set the empty set is a bound on any family of sets ordered by weak inclusion. 3. whence, an estimate of the extent of a given set. 4. (Logic) (of a variable) occurring within the scope of a quantifier that indicates the degree of generality of the open sentence in which the variable occurs; for example, in
(x) (Fx → Gxy),
x is bound, but y is not. Compare free.