A proof of the impossibility of completing infinitely many tasks

Abstract
In this article, I argue that it is impossible to complete infinitely many tasks in a finite time. A key premise in my argument is that the only way to get to 0 tasks remaining is from 1 task remaining, when tasks are done 1-by-1. I suggest that the only way to deny this premise is by begging the question, that is, by assuming that supertasks are possible. I go on to present one reason why this conclusion (that supertasks are impossible) is important, namely that it implies a new verdict on a decision puzzle propounded by Jeffrey Barrett and Frank Arntzenius
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DOI 10.1111/j.1468-0114.2011.01412.x
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References found in this work BETA
On Some Paradoxes of the Infinite.Victor Allis & Teunis Koetsier - 1991 - British Journal for the Philosophy of Science 42 (2):187-194.
An Infinite Decision Puzzle.Jeffrey Barrett & Frank Arntzenius - 1999 - Theory and Decision 46 (1):101-103.
Comments on Professor Benacerraf's Paper.James Thomson - 1970 - In Wesley C. Salmon (ed.), Zeno’s Paradoxes. Bobbs-Merrill. pp. 130--138.

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Citations of this work BETA
Throwing Darts, Time, and the Infinite.Jeremy Gwiazda - 2013 - Erkenntnis 78 (5):971-975.

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Issues Regarding General and Domain-Specific Resources.David Caplan & Gloria Waters - 1999 - Behavioral and Brain Sciences 22 (1):114-122.
Tasks, Super-Tasks, and the Modern Eleatics.Paul Benacerraf - 1962 - Journal of Philosophy 59 (24):765-784.
Tasks and Supertasks.James Thomson - 1954 - Analysis 15 (1):1--13.
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