Escaping an Infinitude of Lions

TL;DR

This paper proves that a man can evade an infinite number of lions in a plane if he runs slightly faster than them, regardless of how many lions there are.

Contribution

It establishes that survival is possible for a man running at speed just above that of lions against an infinite set.

Findings

Man can escape from countably infinite lions if his speed exceeds theirs by any positive amount.

The result holds for any positive epsilon, no matter how small.

The paper provides a strategy for the man's escape in this infinite setting.

Abstract

We consider the following game played in the Euclidean plane: There is any countable set of unit speed lions and one fast man who can run with speed $1+\varepsilon$ for some value $\varepsilon>0$. Can the man survive? We answer the question in the affirmative for any $\varepsilon>0$.