> we don't normally, in our physical world, encounter infinite amounts of anything. I may be missing your meaning, but we encounter distances (e.g. line-segmen

> we don't normally, in our physical world, encounter infinite amounts of anything. I may be missing your meaning, but we encounter distances (e.g. line-segments) all the time; the number of points on a line-sement is equal to the cardinality of the reals. The physical world is full of infinite sets, most of which are uncountable.