Each of those positions is where the point was at some instant or other.

Between the two end positions on the line, the point where the motion began and the point where it stopped, there is no point of the line which does not belong to that series.

We have thus an infinite series of successive positions of a continuously moving point, and in that series are included all the points of a certain piece of line-room." [1] Thus, we are told that, when a point moves along a line, between any two positions of it there is an infinite number of intermediate positions.

Clifford does not play with the word "infinite"; he takes it seriously and tells us that it means without any end: "_Infinite_; it is a dreadful word, I know, until you find out that you are familiar with the thing which it expresses.

In this place it means that between any two positions there is some intermediate position; between that and either of the others, again, there is some other intermediate; and so on _without any end_.