Recent content by Bbkowal

Thank you micromass and pwshafu. I guess I had better study set theory more thoroughly.

I disagree with Micromass. As an example take a proof that the reals between zero and one have a cardinal number of 2^N where N is aleph null: First write the reals in binary notation from 0.000000... to 0.111111... Then the first place after the decimal can take one of two possible values...

I understand the argument for the cantor set end points being countable, but that still does not explain the fact that in order to generate the cantor set an infinite number of end point doublings must take place. If we double something repeatedly N times then we will end up with 2^N things...

The number of end points of the cantor set double each time an iteration is performed, therefore the total number of end points after infinite iterations is ~ 2^N where N is cantor's aleph null. 2^N is, however, c (the number of the continuum) and is therefore uncountable but we know that the...