In a way that is accepted as true without proof or as a basic fundamental principle.
Adverbial form of 'axiomatical,' derived from Greek 'axios' (worthy) via 'axiom.' The '-ally' suffix converts the adjective to an adverb indicating manner or method.
When mathematicians say something 'axiomatically holds true,' they're basically saying 'we're starting here and not arguing about it—everything else builds from this.'
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