The view of infinity as a metaphor, a basic premise of modern cognitivetheory of embodied knowledge, suggests in particular that there may bealternative ways in which one could formalize mathematical ideas aboutinfinity. We discuss the key ideas about infinitesimals via a proceptualanalysis of the meaning of the ellipsis"..." in the real formula .999... = 1.Infinitesimal-enriched number systems accomodate quantities in the half-openinterval [0,1) whose extended decimal expansion starts with an unlimited numberof repeated digits 9. Do such quantities pose a challenge to the unitalevaluation of the symbol ".999..."? We present some non-standard thoughts onthe ambiguity of the ellipsis, in the context of the cognitive concept ofgeneric limit of B. Cornu and D. Tall. We analyze the vigorous debates amongmathematicians concerning the idea of infinitesimals.
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