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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: 8,833
Registered: 1/6/11
Re: Infinity: The Story So Far
Posted: Feb 27, 2014 3:54 PM
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In article <f87bb7ed-8621-4ade-9dcd-7751b490430f@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:
> On Thursday, 27 February 2014 15:14:41 UTC+1, Dan Christensen wrote:
> > On Thursday, February 27, 2014 6:54:55 AM UTC-5, muec...@rz.fh-augsburg.de
> > wrote:

> > > On Thursday, 27 February 2014 10:15:41 UTC+1, Virgil wrote:
> > > > Any set satisfying the Peano postulates can serve as "the" set of
> > > > natural numbers.

> > > Not in mathematics.
> > > This sequence satifies the Peano axioms:
> > > 0, 0.9, 1.8, 2.7, ...
> > > What axiom is violated?

> > The axioms only specify the name of the of the first number.

> And the further numbers are not specified

> > (Even for that, we have some leeway -- usually 0 or 1). In theory, you can
> > choose whatever symbols you like for the rest.


> Only if you know that they shall have the meaning known from childhood - not
> from Peano.


Knowing from childhood is not at all necessary.

For example, one rarely "knows from choldhood" the sequence in base two:
1, 10, 11, 100, 101, 110, 111, 1000, ...

But it is a perfectly legitimate enumeration of members of N

> That would not be mathematics.

WM is not competent to speak for what is or is not MATHEMATICS.
His expertise ceases at the boundaries of WOLKENMUEKENHEIM.

> You do not get the natural numbers unless you
> specify that the differences must be units.


One may not be able to get WM's version of the natural numbers unless
one plays by WM's rules, but, when playing by WM's rules one can not
even get an actually infinite set of naturals like everyone else gets.

And with the von Nuemann naturals, no such a priori specification is
necessary, as it follows automatically from the construction.
--




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
Read Re: Infinity: The Story So Far
Leo Sgouros
2/26/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
William Elliot
3/1/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
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
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
Virgil
2/26/14
Read Re: Infinity: The Story So Far
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
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 show a canonical base-one accounting by induction on base-eleven
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
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
Read the story of numbers
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
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
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/27/14
Read Re: Infinity: The Story So Far
fom
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
Tanu R.
2/27/14
Read Re: Infinity: The Story So Far
Tanu R.
2/28/14
Read Re: Infinity: The Story So Far
Virgil
2/27/14
Read Re: Infinity: The Story So Far
Virgil
2/27/14
Read Re: Infinity: The Story So Far
Tanu R.
2/27/14
Read Re: Infinity: The Story So Far
fom
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/28/14
Read Re: Infinity: The Story So Far
Virgil
2/28/14
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/28/14
Read Re: Infinity: The Story So Far
Virgil
2/28/14
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/28/14
Read Re: Infinity: The Story So Far
Virgil
2/28/14
Read Re: Infinity: The Story So Far
fom
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
Tanu R.
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Virgil
2/26/14
Read Re: Infinity: The Story So Far
Virgil
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
Virgil
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
Read Re: Infinity: The Story So Far
fom
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
fom
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
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
Virgil
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
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
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
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
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
fom
2/27/14
Read Re: Infinity: The Story So Far
Peter Percival
2/27/14
Read Re: Infinity: The Story So Far
fom
2/27/14
Read Re: Infinity: The Story So Far
Peter Percival
2/27/14
Read Re: Infinity: The Story So Far
fom
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
4/7/14
Read Re: Infinity: The Story So Far
Aatu Koskensilta
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
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Virgil
2/26/14
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
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
Virgil
2/26/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
Brian Q. Hutchings
2/26/14
Read Re: Infinity: The Story So Far
Virgil
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
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
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
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
Tanu R.
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/28/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/28/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/28/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/28/14
Read Re: Infinity: The Story So Far
John Gabriel
2/28/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/28/14
Read Re: Infinity: The Story So Far
John Gabriel
2/28/14
Read Re: Infinity: The Story So Far
Sal Honda
2/27/14
Read Re: Infinity: The Story So Far
Wizard-Of-Oz
2/27/14
Read Re: Infinity: The Story So Far
fom
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
fom
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 - JG sloppy axioms
Wizard-Of-Oz
2/27/14
Read Re: Infinity: The Story So Far - JG sloppy axioms
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far - JG sloppy axioms
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2/27/14
Read Re: Infinity: The Story So Far - JG sloppy axioms
thenewcalculus@gmail.com
2/28/14
Read Re: Infinity: The Story So Far - JG sloppy axioms
Wizard-Of-Oz
2/28/14
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2/28/14
Read Re: Infinity: The Story So Far - JG sloppy axioms
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2/28/14
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2/28/14
Read Re: Infinity: The Story So Far - JG sloppy axioms
Wizard-Of-Oz
2/28/14
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Wizard-Of-Oz
2/28/14
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Wizard-Of-Oz
2/28/14
Read Re: Infinity: The Story So Far - JG's axioms allow 2+3=6
thenewcalculus@gmail.com
2/28/14
Read Re: Infinity: The Story So Far - JG's axioms allow 2+3=6
Wizard-Of-Oz
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/28/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/28/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/28/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/28/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/28/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/28/14
Read Re: Infinity: The Story So Far
John Gabriel
2/28/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/28/14
Read The Spaghetti Axioms were meant to...
John Gabriel
2/28/14
Read Re: The Spaghetti Axioms were meant to...
fom
2/28/14
Read Re: The Spaghetti Axioms were meant to...
John Gabriel
2/28/14
Read Re: The Spaghetti Axioms were meant to...
fom
2/28/14
Read Re: The Spaghetti Axioms were meant to...
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2/28/14
Read Re: The Spaghetti Axioms were meant to...
Dan Christensen
2/28/14
Read Re: The Spaghetti Axioms were meant to...
Wizard-Of-Oz
2/28/14
Read Difference between postulate and axiom.
John Gabriel
2/28/14
Read Re: Difference between postulate and axiom.
Harman Kardan
2/28/14
Read Re: Difference between postulate and axiom.
John Gabriel
2/28/14
Read Re: Difference between postulate and axiom.
Wizard-Of-Oz
2/28/14
Read Re: Infinity: The Story So Far
Johnny Oiler
3/1/14
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thenewcalculus@gmail.com
3/1/14
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Dan Christensen
3/1/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/1/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/1/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/1/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/1/14
Read Re: Infinity: The Story So Far
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3/1/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/1/14
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thenewcalculus@gmail.com
3/2/14
Read Re: Infinity: The Story So Far
Wizard-Of-Oz
3/1/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/1/14
Read Re: Infinity: The Story So Far
Wizard-Of-Oz
3/1/14
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thenewcalculus@gmail.com
3/2/14
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Wizard-Of-Oz
3/1/14
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3/1/14
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3/2/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
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3/2/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
John Gabriel
3/2/14
Read Re: Infinity: The Story So Far
Wizard-Of-Oz
3/2/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
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3/2/14
Read Re: Infinity: The Story So Far
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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3/2/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
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John Gabriel
3/2/14
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Dan Christensen
3/3/14
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John Gabriel
3/3/14
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Dan Christensen
3/3/14
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Wizard-Of-Oz
3/3/14
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3/3/14
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Virgil
3/2/14
Read Re: Infinity: The Story So Far - BG's failed attempt at constructing numbers
Wizard-Of-Oz
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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New Balance
3/2/14
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3/2/14
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New Balance
3/4/14
Read Infinity does not exist and Peano was a moron.
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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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Dan Christensen
3/5/14
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3/4/14
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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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Brian Q. Hutchings
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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3/5/14
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Dan Christensen
3/5/14
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Dan Christensen
3/6/14
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3/6/14
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Dan Christensen
3/6/14
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Dan Christensen
3/6/14
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3/5/14
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YBM
3/6/14
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New Balance
3/6/14
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3/6/14
Read poster boy for "let's die-a-log
Brian Q. Hutchings
3/5/14
Read Peano's rot in action for you!
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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
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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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