Proof of Gilgamesh!!!11!! LOL

Not really.  Time for some math.

So, this anon's been doing some reading about infinite sets.  In particular, the Cantor set.  The book I'm reading asserts (and proves - the "consider the numbers in the Cantor set written in ternary" proof, if you're someone who knows these things) that the Cantor set's cardinal number is the same as the real numbers'.

Now, the definition of the Cantor set suggests to me, a neophyte in these matters, that it should consist of rational numbers, in particular those between zero and one (inclusive) with denominator a power of three, and not even all of those.  If it were only rationals, you'd expect it to have the same cardinality as the rationals, i.e. less than the reals.  So, what's the deal here?  Does the Cantor process describe real numbers in the limit kinda like describing real numbers by infinite nests of intervals a la Dedekind?  Is there an alternative method of proof that makes it a little clearer how the definition of the Cantor set winds up spitting out real numbers as well as rationals?

Huh... That is weird. It looks so very countable. I would guess the secret lies in there existing numbers that can't be reached by any finite number of iterations, but only through the limit of infinite iterations (e.g. representing the binary string of an binary irrational number.) That should be what makes it uncountable, at least.
So, yeah. No idea beyond what you said, really.

Assuming wikipedia is right, then all numbers in the Cantor set have an expansion in base 3 consisting entirely of 0 and 2.  Therefore, the following number (base 3) should be in the Cantor set: .0202020202...
=2(.01010101...)
=2((1/9)+(1/81)+(1/729)+...)
=2(1/8)
=1/4

Though this number is rational, it should at least convince you that not all numbers in the cantor set are rational numbers with a denominator that is a power of three.

The above analysis also suggests something else: any number in the Cantor set, when divided by 2, yields another number in base 3 whose expansion consists entirely of 0 and 1.  This is exactly a description of the set of all real numbers in binary.  EG:
.0200002220202... ->
.0100001110101...

tl;dr: lurk moar on wikipedia

http://en.wikipedia.org/wiki/Cantor_set
http://en.wikipedia.org/wiki/Smith-Volterra-Cantor_set (somewhat related, but interesting)

>>1
you faggot i read your post to see the proof of gilgamesh ;'(