Yes Tom,
You have to understand why infinity and singularities are mathematical constructs without concrete physically real counterparts. Ask ordinary people for telling you any countable item. Since they don't think like you in a castle in the air of abstract notions, they will certainly agree on that all tangible items are finite. Well, it is not feasible to count all trees on earth, in particular because it is difficult to decide whether or not an object of consideration is a tree. However, a tree is a real and therefore countable item. The same for the number of stars in a German nursery rhyme: "God the Lord did count them all in order to make sure, not a single one is missing." Cantor is greeting.
Eckard