adj. 1. (of an algebraic structure) consisting of all formal objects satisfying the requisite algebraic conditions without additional relations being imposed; for example, the symmetric group on a set of three elements is not free as a group. See also free group, free module. 2. (of a tree) not having a root (or origin). 3. (Logic) (of a variable) not bound, so that it is at best a place-holder in an open sentence; in some formulations of logic these are interpreted as universally quantified. 4. (of a vector) determined only up to translation; unattached. 5. (of an element of a group) not of finite period.