On Saturday, 21 December 2013 15:13:09 UTC+1, wpih...@gmail.com wrote:
> > So we are back to countable but not listable.
In set theory countable is listable. Anywhere else both is recognized as nonsense because the infinite cannot be counted or listed since there are always infinitly many elements beyond every listed element. > > Basically this involves having your cake and > > eating it. > Set theory involves theology. That's why it is called matheology. > > > Any object that consists only of integers must > > be a subset of the integers (an thus countable), > > but a putative 0/1 > > sequence in which every element is 0 or 1 is only > > a sequence if there is a finite rule. > Correct. That is so because after every given element of the sequence you know that the sequence must be continued (since the given element is not the last one) but you don't know how to continue (without a general rule).