Ineradicably is a term that means impossible to remove or uproot completely. There are several synonyms which can be used in place of ineradicably are: unremittingly, persistently, inveterately, ingrained, indelibly, unequivocally, inerasably, immutably, inalterably, and resolutely. These words express the concept of a situation or quality which cannot be eliminated or changed. For example, ingrained beliefs or habits might be considered ineradicable. Inveterate smokers or alcoholics might also be said to have ineradicable addictions. These words can be used interchangeably with ineradicably to convey a meaning that is fixed and unchanging.