The Collaborative International Dictionary of English v.0.48:

Infinitude \In*fin"i*tude\, n.
   1. The quality or state of being infinite, or without limits;
      infiniteness.
      [1913 Webster]

   2. Infinite extent; unlimited space; immensity; infinity. "I
      am who fill infinitude." --Milton.
      [1913 Webster]

            As pleasing to the fancy, as speculations of
            eternity or infinitude are to the understanding.
                                                  --Addison.
      [1913 Webster]

   3. Boundless number; countless multitude. "An infinitude of
      distinctions." --Addison.
      [1913 Webster]

WordNet (r) 3.0 (2006):

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