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Topic: Infinity: The Story So Far
Replies: 298   Last Post: Apr 7, 2014 7:30 AM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Infinity: The Story So Far
Posted: Feb 27, 2014 4:15 PM
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In article <52803334-ed38-4e9b-8715-7f446379e894@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:
> On Thursday, 27 February 2014 10:00:55 UTC+1, Virgil wrote:
> > In article <7132bb59-31ec-4f71-88a8-cdcb2154affe@googlegroups.com>,
> > mueckenh@rz.fh-augsburg.de wrote:

> > > On Thursday, 27 February 2014 01:48:53 UTC+1, Virgil wrote:
> > > > In article <d2dd2977-8a21-4f88-942b-6bae51ffba5f@googlegroups.com>,
> > > > mueckenh@rz.fh-augsburg.de wrote:

> > > > > You believe that all real numbers R except a countable set D are
> > > > > undefinable.


> > WRONG!

> You have said so at least.

That is a lie. I have been very careful not to say that, because, as
stated, it is not true. The set of all reals is definable, so ther are
no reals which are totally undefinable, they are all collectively
definable but most of them are without any individual definition.

> > > > The reals are COLLECTIVELY defined

> > > That does not make them enumerable.

> > In fact, their verydefinition makes them non-numerable.

> It makes them non-definable.

Then how does WM manage to speak of them at all?

> > > > by the standard definition of the field of real numbers, but
> > > > that collective definition does not guarantee that each of them
> > > > also has an individual definition separable from other
> > > > individual definitions of all other real numbers.



> > > > Similarly, Given a set of naturals numbers ther must be subsets
> > > > of that set which cannot have finite definitions, unless WM can
> > > > drum up more thatn countably many definitions.


> sic!

Until WM can drum up some set which is equinumerous with its power set,
there will be sets not all of whose subsets can be named, and sets not
all of whose members can be named.
--




Date Subject Author
2/25/14
Read Infinity: The Story So Far
Dan Christensen
2/25/14
Read Re: Infinity: The Story So Far
Brian Q. Hutchings
2/25/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
2/25/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
2/26/14
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Leo Sgouros
2/26/14
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ross.finlayson@gmail.com
2/26/14
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William Elliot
3/1/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
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Brian Q. Hutchings
2/26/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
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thenewcalculus@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
Read Re: Infinity: The Story So Far
Virgil
2/26/14
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Dan Christensen
2/26/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/26/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/27/14
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/27/14
Read Re: Infinity: The Story So Far
Virgil
2/26/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
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2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
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Brian Q. Hutchings
2/26/14
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
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mueckenh@rz.fh-augsburg.de
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
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Brian Q. Hutchings
2/27/14
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/27/14
Read Re: Infinity: The Story So Far
Virgil
2/27/14
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
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mueckenh@rz.fh-augsburg.de
2/27/14
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2/27/14
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mueckenh@rz.fh-augsburg.de
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fom
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2/27/14
Read Re: Infinity: The Story So Far
Virgil
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fom
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Virgil
2/28/14
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mueckenh@rz.fh-augsburg.de
2/28/14
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Virgil
2/28/14
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mueckenh@rz.fh-augsburg.de
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fom
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mueckenh@rz.fh-augsburg.de
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2/27/14
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mueckenh@rz.fh-augsburg.de
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Dan Christensen
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2/27/14
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mueckenh@rz.fh-augsburg.de
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2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
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2/27/14
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thenewcalculus@gmail.com
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2/27/14
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thenewcalculus@gmail.com
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2/27/14
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2/28/14
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2/27/14
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2/27/14
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Dan Christensen
2/27/14
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Dan Christensen
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Dan Christensen
2/27/14
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thenewcalculus@gmail.com
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Dan Christensen
2/28/14
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thenewcalculus@gmail.com
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Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
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3/2/14
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Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
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Dan Christensen
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3/2/14
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Dan Christensen
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3/2/14
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Dan Christensen
3/2/14
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3/2/14
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Dan Christensen
3/2/14
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John Gabriel
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Virgil
3/2/14
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3/2/14
Read How I established my axioms.
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3/2/14
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Jürgen R.
3/2/14
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3/3/14
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3/2/14
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3/2/14
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3/4/14
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3/4/14
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3/4/14
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Dan Christensen
3/4/14
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3/4/14
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Dan Christensen
3/4/14
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Dan Christensen
3/4/14
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Dan Christensen
3/5/14
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3/5/14
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3/5/14
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3/5/14
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Dan Christensen
3/5/14
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3/5/14
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3/5/14
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Dan Christensen
3/5/14
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3/5/14
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Dan Christensen
3/5/14
Read No need for spaghetti "axioms".
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3/5/14
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Dan Christensen
3/5/14
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Dan Christensen
3/5/14
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Dan Christensen
3/5/14
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3/5/14
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Dan Christensen
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Read poster boy for "let's die-a-log
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Dan Christensen
3/5/14
Read Re: Peano's rot in action for you!
Peter Percival
3/5/14
Read Re: Peano's rot in action for you!
thenewcalculus@gmail.com
3/5/14
Read Re: Peano's rot in action for you!
Martin Shobe
3/5/14
Read Re: Peano's rot in action for you!
Wizard-Of-Oz
3/5/14
Read Re: Peano's rot in action for you!
Wizard-Of-Oz
3/5/14
Read Re: Peano's rot in action for you!
Wizard-Of-Oz
3/5/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/6/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/6/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/6/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Wizard-Of-Oz
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/12/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/12/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/12/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com

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