The Collaborative International Dictionary of English v.0.48:

Infiniteness \In"fi*nite*ness\, n.
   The state or quality of being infinite; infinity; greatness;
   immensity. --Jer. Taylor.
   [1913 Webster] infinite regress

WordNet (r) 3.0 (2006):

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