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The Collaborative International Dictionary
Inexhaustibleness

Inexhaustible \In`ex*haust"i*ble\, a. Incapable of being exhausted, emptied, or used up; unfailing; not to be wasted or spent; as, inexhaustible stores of provisions; an inexhaustible stock of elegant words.
--Dryden.

An inexhaustible store of anecdotes.
--Macaulay. -- In`ex*haust"i*ble*ness, n. -- In`ex*haust"i*bly, adv.

Wiktionary
inexhaustibleness

n. The quality of being inexhaustible.