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.
1 By definition, completing infinitely many tasks requires getting the number of tasks remaining down to 0. 2 If tasks are done 1-by-1, then the only way to get to 0 tasks is from 1 task, because if more than 1 task remains, then performing a task does not leave 0 tasks. (This reasoning holds in both the finite and infinite cases.) 3 When infinitely many tasks are attempted 1-by-1, there is no point at which 1 task remains. 4 Then from 2 and 3, there is no point at which 0 tasks remain. 5 Then from 1 and 4, it is not possible to complete infinitely many tasks.
Therefore it is not possible to enumerate all rational numbers (always infinitely many remain) by all natural numbers (always infinitely many remain) or to traverse the lines of a Cantor list (always infinitely many remain).