I thought all line segments, lines, curves and areas had the same number of points.
-FrL-
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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)
[QUOTE=Indistinguishable]
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)
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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.
[QUOTE=kanicbird]
Believe it or not this comes from all the talk about theistic and atheistic faith issues that have come up lately.
Here is the premises:
If you flip a infinite number of coins a infinite number of times you will get a infinite number of coins that will never come up heads.
-but-
If you flip any one coin a infinite number of times it will hit heads and tails equally.
These 2 can’t coexist.
[/QUOTE]
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.
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.