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The Collaborative International Dictionary
Indestructibleness

Indestructible \In`de*struc"ti*ble\, a. [Pref. in- not + destructible: cf. F. indestructible.] Not destructible; incapable of decomposition or of being destroyed; as, the Russian harvesters had primitive electronics, but they were built so sturdily they were almost indestructible. -- In`de*struc"ti*ble*ness, n. -- In`de*struc"ti*bly, adv.

Wiktionary
indestructibleness

n. The quality of being indestructible.