In article <email@example.com>, firstname.lastname@example.org wrote:
> > We can easily define a sequence of finite symbols, the decimal symbols > > for the natural numbers, which is not a finite sequence, therefore the > > set of them is not a finite set. > > Nevertheless each symbol can be expressed by a finite number of bits, > reducing this to an alphabet of two letters.
al that does is show that the infinite decimal system can be also expressed as an infinite binary system.
> Moreover every finite expression made of a countable alphabet belongs to the > countable set of all finite expressions made of countable alphabets.
But the set of all subsets of such countably infinite sets is not itself countably infinite. So one still gets uncountably many things. --