Source : Webster's Revised Unabridged Dictionary (1913)

Infinitely \In"fi*nite*ly\, adv.
   1. Without bounds or limits; beyond or below assignable
      limits; as, an infinitely large or infinitely small
      quantity.

   2. Very; exceedingly; vastly; highly; extremely. ``Infinitely
      pleased.'' --Dryden.

Source : WordNet®

infinitely
     adv 1: without bounds; "he is infinitely wealthy" [syn: {boundlessly},
             {immeasurably}]
     2: continuing forever without end; "there are infinitely many
        possibilities" [syn: {endlessly}] [ant: {finitely}]