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Topic: Infinity: The Story So Far
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thenewcalculus@gmail.com

Posts: 1,616
Registered: 11/1/13
Re: How I established my axioms.
Posted: Mar 2, 2014 12:25 PM
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On Sunday, 2 March 2014 19:19:08 UTC+2, Jürgen R. wrote:
> "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


Russell was an incompetent fool next to Euclid. I think you just helped my argument. :-)

To say that the Elements was a masterpiece of logic has been very grossly exaggerated is to say that Russell was a complete imbecile.


Date Subject Author
2/25/14
Read Infinity: The Story So Far
Dan Christensen
2/25/14
Read Re: Infinity: The Story So Far
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Dan Christensen
2/27/14
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Dan Christensen
2/27/14
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thenewcalculus@gmail.com
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Dan Christensen
2/27/14
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thenewcalculus@gmail.com
2/27/14
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Dan Christensen
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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
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Dan Christensen
2/28/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
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2/28/14
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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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3/2/14
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Dan Christensen
3/2/14
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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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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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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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thenewcalculus@gmail.com
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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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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Dan Christensen
3/5/14
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Dan Christensen
3/5/14
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Dan Christensen
3/5/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/5/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/5/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/5/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/6/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/6/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/6/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/6/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/5/14
Read Re: No need for spaghetti "axioms".
YBM
3/6/14
Read Re: No need for spaghetti "axioms".
New Balance
3/6/14
Read Re: No need for spaghetti "axioms".
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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