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From: spudnik on 20 Jan 2010 01:17
yeas, the word, definition, is itself an etonym
of "finite;" congratulation. now, if
you re-de-finite the ellipsis ( ... ),
to mean other than the usual use in practically all
of mathematics, as far as I know -- but, perhaps,
Fermat did not bother to use it -- then
you may be able to create a new de-finite-ion
of the "real number, 1.0000..." (NB:
I have left out the implied seroes to the left,
per Hensel's lemma.)

> When you define Finite-Number precisely, then there is
> no problem with any number such as the fantasy
> of 0.999.... equal to 1, because they are not equal.

thus:
_There are No Electrons_ by What's His Name;
"There certainly R no 'photons,' no matter
what Newton thought about them;" and
There are only 2n electronic ports (for natural "n" !-)

> The French meter was the length of a one-second pendulum measured in
> Parisian gravity to the length and time standards of the era. If it
> had only been a teeny tiny bit smaller... a mere factor of
> 0.9993082...

thus:
"2B or ~2B" ??

> The third possibility is that he's sneaking in a hidden rule or
> two about how the set is constructed, instead of using the
> Axiom alone to do so.

thus:
several have posted references to the non-null results
of the Michelson-Morely Xprmnt; Cahill (?) sites a paper
that gives a l o v e l y graphical comparison
of the "nulls" of M&M and successors (D.C.Miller e.g.);
read it and freak.

thus:
cool; would some one provide a tutorial?

> > the number of self-conjugate partitions of N is the same as the number of
> > partitions of N into distinct odd parts. Is there a way to determine the
> > number S(N;n) of self-conjugate paritions of N given that they all
> > must contain a largest element n?
> It seems to me that S(N; n) = S(N - 2 n + 1).

thus:
I agree with the above pundits;
all you have to do is actually create such a proof, or
you can just "work-through" any that were done,
such as Fermat's -- http://wlym.com --
the creator of the modern theory of numbers,
of which Godel was a rather crude arithmetical usage
-- totally elementary, but rather laborious --
I think. in particular,
Fermat's "reconstruction" of Euclid's "porisms" is supposed
to be exmplary, for a cannonical geometrical proof.

thus:
first of all, did anyone point out that the Archimedean valuation
of "irony" is perhaps a definition of some other (English) word?...
I invite others to supply a better word to his putative de-finite-ion!
I would, again -- at the risk of contributing to any royalties
that AP gets for any one attending to his **** -- like,
to refer to Ore's _Number Theory and Its History_
for a de-finite-ive account of Stevin's revolution
of _The Decimals_, and the reference to it in Munk's treatise
(published by a "vanity press," as he had used
during the Great Depression to publish the first "layman's" account
of aerodynamics.)

--l'OEuvre!
http://wlym.com
From: spudnik on 20 Jan 2010 17:32
anyway, you are trying to throw-out the bathwater
of the impossibly-least-significant digit,
some thing that is just an underflow or overflow condition
in the IEEE-754 specification for floating-point operations,
with the baby of Leibniz's calculus;
to what end?

there seem to be a handful of folks on Usenet,
who worry about Stevin's de-finite-ion of the decimals, and
try to make it into a "new math," when
it is simply the sole ambiguity of them --
doesn't occur in base-one!

thus:
the "100-Model of 'ten to the minus googolplex?...'"
a googolplexth; and, 10^-500 would be the fifth power
of a googolth. if the dood who created the googol were alive,
he'd be freaking on this!

however, the 0.3333..-3 "notation" is a problem;
what in Heck could that mean?

thus:
thus quoth:
The heart of the matter before us, begins with the hypothesis and
experimental validation of the Ampère angular force. Before the
discovery by Oersted and Ampère of the effective equivalence of a
closed current and a magnet, it appeared that the pairwise forces
between bodies were governed by the same law of universal
gravitation,
which Johannes Kepler had first noted in his 1609 New Astronomy.1 At
the time in question, 1819-1821, three known phenomena appeared to
behave according to the assumption that the force between two bodies
was determined according to the inverse square of their distance of
separation. Apart from gravitation, these were the phenomena of
electrostatic, and magnetic attraction and repulsion, investigated
especially by Coulomb and Poisson.

In all three cases, there was some question as to the perfect
validity
of the inverse-square assumption. In the case of magnetism, the
impossibility of separating the two opposite poles, made exact
measurement of the pairwise relationship of one magnet to another
always inexact. This problem of the existence of a “third body” did
not entirely go away, even in the case of the most carefully observed
of these phenomena, gravitation.

The Ampère Angular Force
http://www.21stcenturysciencetech.com/articles/spring01/Electrodynami...

--les OEuvres!
http://wlym.com
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