If they are infinite, then there should at least be a well-defined way to take a limit (or one of its generalizations), which amounts to nearly the same thing, constructing a sequence of ratios of finite numbers and proving convergence.
If they are infinite, then there should at least be a well-defined way to take a limit (or one of its generalizations), which amounts to nearly the same thing, constructing a sequence of ratios of finite numbers and proving convergence.