Date: Feb 5, 2013 5:04 PM
Author: Virgil
Subject: Re: Matheology � 203
In article

<ec3e530e-a325-408d-851e-d236b1106f99@z9g2000vbx.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> 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.

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