There can, then, be no last term to the series; _i.e._ what the point is doing at the very last is absolutely indescribable; it is inconceivable that there should be a _very last_.
It was pointed out many centuries ago that it is equally inconceivable that there should be a _very first_.

How can a point even begin to move along an infinitely divisible line?
Must it not before it can move over any distance, however short, first move over half that distance?
And before it can move over that half, must it not move over the half of that?
Can it find something to move over that has no halves?
And if not, how shall it even start to move?
To move at all, it must begin somewhere; it cannot begin with what has no halves, for then it is not moving over any part of the line, as all parts have halves; and it cannot begin with what has halves, for that is not the beginning.

_What does the point do first ?_ that is the question.
Those who tell us about points and lines usually leave us to call upon gentle echo for an answer.
The perplexities of this moving point seem to grow worse and worse the longer one reflects upon them.

They do not harass it merely at the beginning and at the end of its journey.

This is admirably brought out by Professor W.K.Clifford (1845-1879), an excellent mathematician, who never had the faintest intention of denying the possibility of motion, and who did not desire to magnify the perplexities in the path of a moving point.