Say an object is to travel from point A to point B, a finite distance of 2 meters. Say the object travels at 1m/s.
After 1 meter the speed of the object is halved. After another half of the previous distance the speed is halved again, and so on.
So for each term in the infinite series 1 + 1/2 + 1/4 + 1/8 + ..., the term represents the distance the object travels in meters before the speed is halved.
Now apparently the object does eventually reach point B, but it takes an infinite amount of time to do so.
Yet infinity has no end.
So if the the object does ever reach point B, wouldn't that mark the end of the infinite length of time that it took to reach it and wouldn't that contradict with the definition of infinity?
Yet if we say it never reaches point B, which is to say that there is no point in time that it reaches point B because that point in time would mark an end to infinity, then isn't it consistent with what we mean by infinity?