Date: Feb 5, 2013 5:04 PM
Subject: Re: Matheology � 203
WM <firstname.lastname@example.org> 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
> with connecting edges as a guides for the eye does not make any
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.