I was inspired by this wikipedia article invoking a notion of a "Supertask" (informally, an infinite sequence of operations performed in a finite amount of time) to pose Zeno's paradox.
To my understanding, the paradox is posed as this: since motion must cross half of the path between A and B, then half the path therein, and so on, motion is a Supertask.
My question is this: can't we apply the same halving argument to time, so that an infinite number of time-segments is used in the process of motion? Therefore, motion wouldn't be a Supertask. (A little more formally: if both time and 1-dimensional space are assumed to be segments of the reals, then any halving argument constructing infinite cells out of these segments can be applied to both time and space. Then we're only traversing an infinite sequence of cells of space in infinite cells of time, which is not a supertask.)
What's wrong with this argument? (Or, does it work?)
