The quality or property of being able to be added; the capacity to undergo addition or combination.
Formed from 'addable' plus the suffix '-ity' (from Latin -itas); compounds 'add' (from Latin addere meaning to put to) with modern English morphology.
Mathematicians and physicists need 'addability' to describe which things can be combined and which can't—it's a boring word that points to something profound: not everything in nature combines easily.
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