Physicist frequently use infinity when talking about fields (ex. V = integral of E*dr from 0 to infinity) but if the fields were infinite, be they gravitational or electric, they would span the entire universe and all things effected by it would collapse into a single, crushing point. This has clearly not happened and is not happening. QED, infinity is not real.
>The Paradoxes of Motion
>Achilles and the tortoise...
Did you even look at the page you linked?
>The dichotomy paradox
Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.
Since the distance to the bus is Finite, Homer can make it!