Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Distinguishability argument x Cantor's arguments?
Replies: 15   Last Post: Jan 9, 2013 4:32 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Distinguishability argument x Cantor's arguments?
Posted: Jan 3, 2013 4:31 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 2 Jan., 22:19, Zuhair <zaljo...@gmail.com> wrote:
>
>

> > On the other hand Cantor have presented many arguments all of which
> > are rigorously formalized in second order logic under full semantics,
> > and those arguments PROVED that there are uncountably many reals

>
> that can be distinguished by their finite initial segments.

A decimal, or other base, expression is not a actually a number but
merely a numeral, a representation of or name for a number.

Actually, no real can be distinguished from ALL others by ANY finite
initial segment of its decimal, or other base, representation.
> >
> > So which one we to believe?
> >
> > The answer is Cantor's of course!

>
> So let us believe that uncountably many real numbers can be
> distinguished by their countably many finite initial segments

Only in WMytheology is ANY real distinguishable from all others by ANY
finite initial segment of its decimal, or other base, representation.

> because
> no infinite diagonal of a Cantor list can be defined other than by its
> finite initial segments (or a finite definition).

A finite definition can determine infinitely many digits in a real
number's decimal, or other base, representatoin.

> because Cantor by distinguishing real nunbers "proved" the existence
> of indistinguishable "real" numbers. (He would rotate in his grave

After reading WM's misrepresentation of is ideas, quite likely.
>
> > Because Cantor's arguments are very clear, and are formalizable in an
> > exact manner, so they are quite understandable and obvious. While the
> > distinguishability argument of mine is actually ambiguous and shredded
> > in mystery.

>
> No, every sensible formalization requires finite distinguishability.
>

> > The Consideration step in that argument and the analogy of
> > that with the Generalization step in that argument is really just an
> > intuitive leap nothing more nothing less.
> >
> > This only demonstrates how common intuition fail at absolute infinity.

>
> This demonstrates that Cantor's argument has created thousands of
> matheologians who have a block in their brains.

With WM being a primary example of brain blockage!
--