Infinite means without any end." But really, if the case is as stated, the point in question must be at a desperate pass.

I beg the reader to consider the following, and ask himself whether he would like to change places with it:-- (1) If the series of positions is really endless, the point must complete one by one the members of an endless series, and reach a nonexistent final term, for a really endless series cannot have a final term.
(2) The series of positions is supposed to be "an infinite series of successive positions." The moving point must take them one after another.

But how can it?
_Between any two positions of the point there is an infinite number of intermediate positions_.

That is to say, no two of these successive positions must be regarded as _next to_ each other; every position is separated from every other by an infinite number of intermediate ones.

How, then, shall the point move?
It cannot possibly move from one position to the next, for there is no next.