Re: Cantor Confusion

Newberry wrote:
paths edges
level 1: 2 = 2^1 2
level 2: 4 = 2^2 6
level 3: 8 = 2^3 14

level n: 2^n (not sure what the formula is)

Does the ratio edges/paths converge to 2 for n --> infinity?

Yes, as WM is fond of repeating ad nauseum.

It certainly makes it highly couterintutive that there are more paths
then edges although I do not know if it generates a flat contradiction.

Yes, it is counterintuitive (depending on your intuition). No, there is
no contradiction. You can't take limits without justification. Here is a
nice fallacy of WM's from page 5 of
http://www.arxiv.org/pdf/math.GM/0403238: Group the natural numbers
greater than 1 as follows.

(2) (3 4) (5 6 7 8) ...

If we number the groups starting with zero, then there are 2^n numbers
in group n. So, for finite n, we must have

|N| >= |group n| = 2^n.

Now, let n go to infinity to get

aleph_0 >= 2^{aleph_0}.

--
David Marcus
.