The Collaborative International Dictionary of English v.0.48:

Unbounded \Un*bound"ed\, a.
   Having no bound or limit; as, unbounded space; an, unbounded
   ambition. --Addison. -- Un*bound"ed*ly, adv. --
   Un*bound"ed*ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

unboundedness
    n 1: the quality of being infinite; without bound or limit [syn:
         infiniteness, infinitude, unboundedness,
         boundlessness, limitlessness] [ant: boundedness,
         finiteness, finitude]