In article <email@example.com>, firstname.lastname@example.org wrote:
> > I take a Countable Infinite Set, something like the Natural Numbers. > > Which one cannot be defined by bits? What is the advatage over the binary > alphabet?
That one can in ordinary language finitely define both infinite and even uncoutably infinite sets. > > > > > > > > > > If its Well Constructed that all you need. > > > > > > > > > > It has to be applied. But in order to shorten your phantasies, let us fix > > > the constraints. > > > > > > > > You may "fix" what you please. > > > > Howere, those of us who engage in Mathematics already know the System we > > work within. > > But you have not yet known the fact that every natural number can be > expressed by a finite number of bits?
So can a great many, though not all, infinite sets of natural numbers be expressed by finite definitions.
> Everything that can be mentioned in the mathematical discourse in English > (or any other language that is derived from English or can be translated > into English) belongs to a countable set.