Sure, all the nontrivial ones have the cardinality of the continuum. But the world is full of trivialities: clearly, the empty set has only 0 points and the North Pole has only 1 point, in contrast to the border of India with its infinitely many points. (Specifically, continuum-many, as opposed to, say, the set of points with rational longitude and latitude, which also has area 0, like all of these, but with only a countably infinite number of points)
Well hell, that sounds like a dare!
(Back in a while.)
I totally misread your post. I thought you had said the border has the same area as the entire ice shelf up north around the north pole. And I just skipped the part about the empty set, thinking I had your point already.
Sorry about that!
-FrL-
Both statements are the same logic. In the first statement each coin will sometimes be heads and sometimes be tails. There are only more coins in the first statement than the second. Otherwise they are identical, and can coexist.
Why am I discussing this?
kanicbird is right to say that the two statements can’t coexist; the first statement implies that some coin never comes up heads. The second statement implies that every coin eventually comes up heads. Those two are very clearly incompatible.
The rest of my response to that post is found here. The gist of it is that there aren’t good probabilistic grounds for accepting the first statement as a given, and, in fact, there are very strong probabilistic grounds for rejecting it in many cases.