It’s the same paradox as you see in the following anecdote:
If a rabbit hops halfway from his position to a carrot in one second, then half the remaining distance in the next second and half the remaining distance in the next, etc., how long will it take the rabbit to reach the carrot? Answer: forever. His velocity approaches zero since the distance he covers approaches zero while the time remains constant.
If you define the coastline down to the individual grains of sand on the beach and even beyond that, to the very atomic level, it can be argued that the distance approaches infinity. But of course that is absurd, since APPROACHING infinity is not the same as infinity. 10 ^^ x is a very large number, depending on x, but it is still not infinite.
No... I think it's infinite. Unless at some point nothing can ever get any smaller... which of course never happens. The rabbit can always go halfway, forever. He never reaches the carrot.