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The Collaborative International Dictionary
Ineradicably

Ineradicably \In`e*rad"i*ca*bly\, adv. So as not to be eradicable.

Wiktionary
ineradicably

adv. In an ineradicable manner

Usage examples of "ineradicably".

These and a thousand other things all built the picture of the city in his mind, until now it possessed him and had got somehow, powerfully, exultantly, ineradicably, into everything he did or thought or felt.