Let's say we decide to race on a track 1000km long. You are a 100 times faster than me, meaning if we both start at the beginning you obviously win. To make things more fair you give me a head start of 1m. The distance is still very small, meaning you will obviously win.
A few premises:
-For you to win the race you need to overtake me
-To overtake me you need to reach a point of equivalence
-If there is no point of equivalence you can't beat me
Let's assume it takes you 1 second to reach 1m. However in that 1 second, I would have travelled a distance forward-lets say I am now at 1.01m. You haven't caught up to me- I'm still 0.01m ahead of you. It takes you 0.01s to travel that 0.01m. But in that 0.01 s I would have travelled 0.0001m, meaning I'm still ahead of you. Therefore you can never catch up to me- the distance between us will get infinitesimally small, but never 0. Therefore since you can't catch up to me, you can never win.
This obvious paradox has been resolved through the fact that an infinitesimal series adds up to one- however, doesn't thid simply prove both people will finish the race? How does it prove the faster person will win?
Please don't simply give me a linear solution. I do not want to know when the faster person catches up - I want to know the mathematical flaw in the paradox's logic.