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ABSTRACT
In this paper, we analyze the Achilles-Tortoise paradox, which denies the overtaking of the slowest runner (Tortoise) by the quickest runner (Achilles) because the pursuer must first reach the point whence the pursued started, so the slower must always hold the lead. The paradox translates into a requirement for the quicker to complete one by one an infinite sequence of distinct runs in a finite time to overtake the slower. This feat is impossible because the infinite sequence of distances contains no final distance to run, and the time to complete such a feat is not enough. However, we know better that in a race, the quickest always overtakes the slowest. Then why does the argument say otherwise? There should be logical flaws in its argumentation. Therefore, after an analysis of the paradox, we investigate the existence of such a flaw that exists in the argument itself or in the inferences its premises make. In addition to this, we present the new mathematical solution based on open balls in real Euclidean space, which shows that only a finite number of runs are needed by the quickest to overtake the slowest.
Acknowledgements
The authors acknowledge the technical assistance and every kind of unconditional cooperation from the two departments to which the authors belong. They also express their gratitude to the anonymous reviewers for their helpful suggestions, which helped to improve the quality of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).