Adverb
In an inveterate manner or degree.
Source: Webster's dictionaryCreatures inveterately wrong in their inductions have a pathetic but praiseworthy tendency to die before reproducing their kind. Willard van Orman Quine
Nietzsche was an inveterately religious thinker, whose incessant attacks on Christian beliefs and values attest to the fact that he could never shake them off. John N. Gray