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Hmm sounds like Zeno's Arrow Pardox. Arrow must travel half the distance before it can reach the target, and half again and again on infinitum.
Giving 1 - 1/2^n < 1 making continuous motion impossible. Thats why we have infinity to link the Discrete and the continuous without it everything falls apart. As middy rightly pointed out ultimately the limit would give you a perfect arc and zero error. or 1/2^n as n approaches infinity becomes zero. Aristotle responded to this paradox with similar argument in his aptly titled book Physics. Its not Calculus (Newton) its older than that.
Regards
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