Source : Webster's Revised Unabridged Dictionary (1913)

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.

Source : WordNet®

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