If an object halves its speed every second (but never gets to 0), will it eventually get from point A to point B? There is a ball that starts at point A on a line and moves toward point B. Every second, it moves half of the distance left, but never stops moving:!diagram Etc. Would the ball ever reach point B? In one perspective, you could argue that since the ball is perpetually moving, it will reach the end sometime. You could also argue that the ball would never reach the end because it would always be moving half the distance left, never the full. Which is correct? To me, I think that if something is constantly advancing, it would eventually get from A to B. Does it work that way? If it does, at what time would the ball reach the end? Thanks for the help.

After any finite amount of time, the ball will not be at the point $B$. In fact, after $n$ seconds, the ball will travel $1 - \frac{1}{2^n}$ of the full distance between $A$ and $B$. This is because after one seconds, the ball travels a distance of $\frac12$, after $2$ seconds, it travels $\frac12 + \frac 34$, and after $n$ seconds, it travels

$$\sum_{i=1}^n \frac1{2^i} = 1 - \frac{1}{2^n}$$

So, what is wrong with your logic? You say "if something is constantly advancing, it will eventually get from $A$ to $B$", which is false. Your example shows quite clearly that even if something is constantly advancing, if the amount it is advancing by is decreasing, it may never reach its destination.