Paradox Part 2

Never give your opponent a headstart.

Let's paint you a simple situation.

The arrogant rabbit gives the slow moving tortoise a headstart in a race.
It grants the tortoise a 1km headstart.

Now let's assume certain facts about the rabbit and the tortoise.

1) The rabbit and the tortoise move at constant speed, without any acceleration.
2) The rabbit moves at a speed faster than the hare.

Now. Suppose the rabbit is 1km behind the tortoise.
After certain amount of time has elapsed, naturally the rabbit reaches the 1km mark, the point where the tortoise had a headstart and the point where it started the race from. However in that span of time, the tortoise moves a certain amount of distance further forward from the 1km mark, thereby still ahead of the rabbit.

Repeat this process again for another frame of time. The rabbit now leaves the 1km mark to reach the point where the tortoise has left off previously. However, the tortoise once again remains ahead of the rabbit in the race as it inches forward with those steady 4 stumpy legs.

It seems, the rabbit never ever catches up with the tortoise, if we continually break down the time frames into smaller and smaller intervals. In other words, the rabbit has infinite number of points to catch up, points where the tortoise left off previously in the previous time frame.

What's the problem here?

Space has no tolerance for infinity. Like how we postulate that 2 parallel train tracks appear to meet in the end of the horizon.
Pretty dumb when [-inf,inf] is defined in complex calculus.