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Topic: Uncountability of the Real Numbers Without Decimals
Replies: 110   Last Post: Dec 10, 2013 4:33 AM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Uncountability of the Real Numbers Without Decimals
Posted: Dec 5, 2013 4:32 PM

WM <wolfgang.mueckenheim@hs-augsburg.de> wrote:

> Am Dienstag, 3. Dezember 2013 19:56:05 UTC+1 schrieb Zeit Geist:
> > On Tuesday, December 3, 2013 4:42:54 AM UTC-7, WM wrote:
> >

> > > Am Montag, 2. Dezember 2013 21:41:33 UTC+1 schrieb Zeit Geist:
> >
> > >
> >
> > > > > It is impossible eneumerate all rational numbers, i.e.,
> > > > > to remove all rationals from the state of being not enumerated to the
> > > > > state of being enumerated.

Maybe so in WM's wild weird world of WMytheology,
but outside of WMytheology it is quite easy to do.

> >
> > So does the Set of Natural Numbers, but I can still say, "For All n e N,
> > ... ".

>
> chuckle.
> Of course you can say so. But that does not change any mathematical facts.

Nor does WM's unsupported and unsupportable objection prove his case.

> > Suppose for some Property phi, that For Every n e N, phi(n) is the case.
> >
> > Hence, there is NO Natural Number, m, such that ~phi(m) is the case.
> >
> > Therefore, For All n e N, phi(n) is the case.
> >
> >
> >
> > Unless, of course, you reject the Law of the Excluded Middle.
> >

> I do not. You can state that every natural number is either even or od. But
> you cannot "take" most of the natural numbers for any purpose.

"Most" of them is no less than all but finitely many of them, so I find
it quite true to take it that most of them require more than a single
decimal digit to represent tnem.

> > From this we can form function from N to other Sets. This, we can prove
> > that the Set of Rational Numbers are Not Countable.

Actually the set of rationals is countable by the standard definition of
being "countable".
> >
> Have you a definition of "set". Who told you that you can take all natural

Common sense, which WM lacka.

> > No, there could be last Rational in my ordering, say q_l. However, the Set
> > Q \ {q_l} must contain a Sub-Order isomorphic to omega, the Order Type of
> > the Natural Numbers.

>
> First answer whether you have been able to take a natural number that does
> not belong to the first 0 %.

The empty set is 0% of any set except itself.
And until WM can demostrate 1% and other percents of |N, his 0% is not a
defineable subset of |N, so does not exist.

> >
> > > There is no way to circumvent this simple fact. Closing eyes or stamping
> > > feet or shouting axioms will not help.

Which is why WM will always fail.
> >
> >
> >
> > You're the one who seems to be stamp his feet and shouting, "Infinity Can
> > Not Be Completed.".

>
> No. I know simply that all you boast to use belongs to a 0-%-set.

--

Date Subject Author
12/2/13 Tucsondrew@me.com
12/2/13 William Elliot
12/2/13 Tucsondrew@me.com
12/2/13 G. A. Edgar
12/2/13 Tucsondrew@me.com
12/2/13 wolfgang.mueckenheim@hs-augsburg.de
12/2/13 gnasher729
12/2/13 wolfgang.mueckenheim@hs-augsburg.de
12/2/13 Virgil
12/2/13 Tucsondrew@me.com
12/2/13 Virgil
12/3/13 wolfgang.mueckenheim@hs-augsburg.de
12/3/13 Tucsondrew@me.com
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Virgil
12/3/13 Virgil
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Tucsondrew@me.com
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 Virgil
12/5/13 Virgil
12/10/13 Robin Chapman
12/2/13 Virgil
12/2/13 wolfgang.mueckenheim@hs-augsburg.de
12/2/13 Virgil
12/3/13 wolfgang.mueckenheim@hs-augsburg.de
12/3/13 Virgil
12/2/13 Tucsondrew@me.com
12/3/13 wolfgang.mueckenheim@hs-augsburg.de
12/3/13 Tucsondrew@me.com
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Tucsondrew@me.com
12/5/13 Michael F. Stemper
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 Virgil
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Tucsondrew@me.com
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Virgil
12/6/13 Brian Q. Hutchings
12/7/13 Brian Q. Hutchings
12/7/13 Brian Q. Hutchings
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 fom
12/7/13 albrecht
12/7/13 fom
12/7/13 ross.finlayson@gmail.com
12/8/13 albrecht
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 fom
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 fom
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 Virgil
12/7/13 fom
12/8/13 Virgil
12/7/13 Virgil
12/7/13 Virgil
12/7/13 Virgil
12/8/13 albrecht
12/6/13 Virgil
12/6/13 Virgil
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 Virgil
12/5/13 Virgil
12/3/13 Virgil
12/3/13 Michael F. Stemper
12/3/13 Virgil
12/3/13 fom
12/2/13 Tucsondrew@me.com
12/2/13 wolfgang.mueckenheim@hs-augsburg.de
12/2/13 Virgil
12/3/13 wolfgang.mueckenheim@hs-augsburg.de
12/3/13 Virgil
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Virgil
12/2/13 Virgil
12/2/13 Tucsondrew@me.com
12/3/13 wolfgang.mueckenheim@hs-augsburg.de
12/3/13 Virgil
12/3/13 wolfgang.mueckenheim@hs-augsburg.de
12/3/13 gnasher729
12/3/13 wolfgang.mueckenheim@hs-augsburg.de
12/3/13 gnasher729
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Virgil
12/3/13 Virgil
12/3/13 Virgil
12/5/13 gnasher729
12/3/13 Tucsondrew@me.com
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Tucsondrew@me.com
12/5/13 Tucsondrew@me.com
12/5/13 Virgil
12/3/13 wolfgang.mueckenheim@hs-augsburg.de
12/3/13 Tucsondrew@me.com
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Tucsondrew@me.com
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 Virgil
12/8/13 wolfgang.mueckenheim@hs-augsburg.de
12/8/13 Virgil
12/5/13 Virgil
12/3/13 Virgil
12/2/13 ross.finlayson@gmail.com
12/4/13 ross.finlayson@gmail.com
12/3/13 albrecht
12/3/13 Tucsondrew@me.com
12/5/13 albrecht
12/5/13 Tucsondrew@me.com