ineradicably

/ˌɪnɪˈrædɪkəbli/
adverb
  1. In a way that is impossible to remove, destroy, or eliminate.
    • Pollution has ineradicably altered the landscape of the region.
    • The values she learned as a child were ineradicably embedded in her character.
    • The two families were ineradicably linked by generations of shared history.
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