In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 4 Feb., 20:31, fom <fomJ...@nyms.net> wrote: > > On 2/4/2013 2:15 AM, WM wrote: > > > > > > > > > 2) An uncountable set has (infinitely many) more elements than a > > > countable set. > > > > By "more," you mean that the construction of a new name > > may be accomplished and by "infinitely many" you mean that > > consecutive constructions can always be performed sequentially > > without end from any initial finite configuration of names. > > More means more than all rational points of the universe. > Gödel and Cohen doubted the continuum hypothesis. They estimate the > cardinality of the continuum as being muchg larger.
Which, if so, would only make WM even more wrong than he already is. > > > > > 3) Every real number has at least one unique representation as an > > > infinite binary string (some rationals have even two representations > > > but that's peanuts). > > > > By "uniqueness", you mean there is a strategy for > > constructing names that always allows you to differentiate > > a single object from a plurality on the basis of "naming" > > Yes. If you cannot select a particulat number like 3/4 or pi, you > cannot work with it. > > > > > 4) In many cases the string cannot be defined by a finite word. > > > > What would be the limitation here? Is it the negative logic > > of "since there are more numbers than names..."? > > Of course. > > > > > 5) Without loss of information the first bits of two strings, if > > > equal, need not be written twice. > > > > This starts to become a little problematic. Now, your numbers > > are turning into classes of numbers. And, your names are > > turning into the names for canonical representatives of those > > classes if the partition is viewed as an equivalence partition. > > Don't see problems where no problems are. > Whether I write > 3.14000... and 3.14159... > or write > 000... > 3,14 > 159... > with connecting edges as a guides for the eye does not make any > difference.
That would depend on the context in which you write.
If you are writing in a linear context, as most writing is done, then your "3.14000... and 3.14159..." fits in nicely, but the other does not. --