The Infinite Binary Tree (see left-hand figure) has countably many nodes and uncounbtably many paths.
(1) If we look at the upper levels only, then between root node and level n we can distinguish 2^(n) paths and 2^(n+1) - 1 nodes. Classical mathematics would find that in the limit there are twice as many nodes as paths.
(2) If we delete the paths (see right-hand figure) but fix three infinite ribbons to every node instead, then every level is passed by more ribbons than paths. Nevertheless the set of passing ribbons is countable in the limit, the set of paths is uncountable in the limit.
