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

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Jürgen R.

Posts: 242
Registered: 12/13/04
Re: How I established my axioms.
Posted: Mar 2, 2014 12:19 PM
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"John Gabriel" schrieb im Newsbeitrag
news:5e7e7e68-21d3-446c-99ee-367a3239cc53@googlegroups.com...

Listed below are the Axioms of magnitude:


Book V, Def. 1:
1. A magnitude is the idea of size of extent. We can either tell that two
magnitudes are equal or not. If we can tell they are not equal, then we know
which is smaller or bigger, but we can't tell how much bigger or smaller.
This is called qualitative measurement (without numbers).

Book V, Def. 3:
2. We can form ratios of magnitudes. AB : CD where AB and CD are line
segments. The expression AB : CD means the comparison of magnitudes AB and
CD.

Book VII, Def. 1
3. A ratio of equal magnitudes, say AB : AB or CD : CD allows us to use
either as the standard of measurement, that is, the unit. The unit is a
ratio of equal magnitudes.

Book VII, Def. 2
4. The unit enables us now to compare AB and CD if both are exact multiples
of the unit that measures both. We can now perform quantitative measurement,
because we can tell how much greater AB is than CD or how much less AB is
than CD.

Book VII, Def. 3 - 5
5. Finally, if a magnitude is only part of a unit, then we arrive at a ratio
of numbers, say AB : CD where AB and CD are multiples of the unit. AB : CD
now means the comparison of numbers AB and CD. When we write AB/CD, it is
called a fraction.


So in fact, anyone who disagreed with me, was actually disagreeing with
Euclid himself! Tsk, tsk. You should now learn from the terrible folly of
your ways. :-)

====================================================================

It has been customary when Euclid, considered as a text-book, is attacked
for his verbosity
or his obscurity or his pedantry, to defend him on the ground that his
logical excellence
is transcendent, and affords an invaluable training to the youthful powers
of reasoning.
This claim, however, vanishes on a close inspection. His definitions do not
always define,
his axioms are not always indemonstrable, his demonstrations require many
axioms of which
he is quite unconscious. A valid proof retains its demonstrative force when
no figure is drawn,
but very many of Euclid's earlier proofs fail before this test.

...[several examples of the above]

Many more general criticisms might be passed on Euclid's methods, and on his
conception of
Geometry; but the above definite fallacies seem sufficient to show that the
value of his work
as a masterpiece of logic has been very grossly exaggerated.

Bertrand Russell




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
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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
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mueckenh@rz.fh-augsburg.de
2/27/14
Read Re: Infinity: The Story So Far
fom
2/27/14
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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
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thenewcalculus@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
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fom
2/27/14
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Peter Percival
2/27/14
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fom
2/27/14
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Peter Percival
2/27/14
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fom
2/27/14
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thenewcalculus@gmail.com
4/7/14
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Aatu Koskensilta
2/27/14
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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
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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
Dan Christensen
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
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
Read Re: Infinity: The Story So Far - JG sloppy axioms
Dan Christensen
2/28/14
Read Re: Infinity: The Story So Far - JG sloppy axioms
Wizard-Of-Oz
2/28/14
Read Re: Infinity: The Story So Far - JG sloppy axioms
Wizard-Of-Oz
2/28/14
Read Re: Infinity: The Story So Far - JG's axioms allow 2+3=6
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
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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...
John Gabriel
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
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
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
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/2/14
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Wizard-Of-Oz
3/1/14
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Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/1/14
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Wizard-Of-Oz
3/1/14
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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
thenewcalculus@gmail.com
3/2/14
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Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
John Gabriel
3/2/14
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Wizard-Of-Oz
3/2/14
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Dan Christensen
3/2/14
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thenewcalculus@gmail.com
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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3/2/14
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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
Read Re: How I established my axioms.
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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Wizard-Of-Oz
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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ross.finlayson@gmail.com
3/5/14
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Dan Christensen
3/5/14
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ross.finlayson@gmail.com
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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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
3/5/14
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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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thenewcalculus@gmail.com
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!
thenewcalculus@gmail.com
3/5/14
Read Re: Peano's rot in action for you!
Dan Christensen
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!
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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