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The Collaborative International Dictionary
Irredeemableness

Irredeemable \Ir`re*deem"a*ble\, a. Not redeemable; that can not be redeemed; not payable in gold or silver, as a bond; -- used especially of such government notes, issued as currency, as are not convertible into coin at the pleasure of the holder. -- Ir`re*deem"a*ble*ness, adv.

Wiktionary
irredeemableness

n. The quality of being irredeemable.