Prove known can reach the end line of a race?

Answer 1

I think the question is Prove no-one can..., etc. This idea was proposed millenia ago by the Greek thinker Zeno, and is called "Zeno's paradox". The idea was that the runner reaches 1/2 way, then 3/4, 7/8, 15/16, etc. and must therefore never reach the end. It wasn't "proven" beyond the idea of being an interesting apparent paradox which is easily dispelled when one considers that, yes, the runner does reach all those points, but that fact needn't imply a limit on his motion. There is more complexity to the thinking than my summary indicates, however, and you may be interested to read the discussion in the reference.

Answer 2

I don't understand your question.