WM wrote: > But how can we explain that the result > is not influenced by those paths? In my opinion by > recognizing that such paths do not exist.
"result ... not influenced by those paths"? I disagree. Without those paths (like 0.111...) you are able tu enumerate, but taking care of all of them brings you into trouble. It's *them* which are the difficult part. Listing the finite subsets of the natural numbers is easy: just sort by their number of elements and within the sets of equal size order the sets lexicographical.
Those sets influencing the result, I am not forced to disbelieve in the existence of them.