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The Collaborative International Dictionary
Unboundedness

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.

Wiktionary
unboundedness

n. The condition of being unbounded

WordNet
unboundedness

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