system
Given the following post, respond as if you're commenting on Reddit:
human
Is there a theoretical limit for human performance?

This question is inspired by a Roger Bannister quote:

It is a paradox to say the human body has no limit. There must be a limit to the speed at which men can run. I feel this may be around 3:30 for the mile. However, another paradox remains – if an athlete manages to run 3:30, another runner could be found to marginally improve on that time.

Is there any scientific evidence that there is indeed a performance limit for the human body as it currently exists? Or is it that marginal improvements can always be made?
gpt
The answer would came from mathematics, specifically convergence of limits. Long story short, there are two ways a series of numbers can go if you let it run a long time. Stuff like:

1 + 2 + 3 + 4 + 5... will keep getting bigger, and eventually reach infinity (or make a bloody good attempt, anyways).

On the other hand,
1 + 1/2 + 1/4 + 1/8 + 1/16 .... 
will not. Think Zeno's paradox. No matter how much you keep running the series, it'll still be a tiny bit less then 2. 

You can track the improvements the athletes make to the record as a series, and it's quite likely that the bigger the record gets, the smaller the iprovements are, eventually leading to a finite limit.