Examples of problems that are easier in the infinite case than in the finite case. I am looking for examples of problems that are easier in the infinite case than in the finite case. I really can't think of any good ones for now, but I'll be sure to add some when I do.

Burnside problem
The solution for Burnside problem in the following formulation:

For which positive integers $m$, $n$ is the free Burnside group $B(m, n)$ finite?

is not known for any $m$, $n$, but there are some results for infinite cases:


*

*$B(m,n)$ is infinite for all odd $n > 665$

*$B(m,n)$ is infinite for even $n > 2^{48}$ and $n$ divisible by $2^9$

*$B(m,3)$, $B(m,4)$ and $B(m,6)$ are finite for all $m$


And the example for the question is $B(2,5)$, for which it is not known whether it is finite. $B(2,5)$ also has the smallest $m$ and $n$ for which the problem remains open.
