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From: Archimedes Plutonium on 21 Jan 2010 14:41


Archimedes Plutonium wrote:

>
> P.S. the next time any person tries to persuade you that the Successor
> cannot create
> an infinite-number. Then just turn the tables on him by saying " so
> you think that the
> series 1 + 1 + ....+ 1 does not go to infinity but is equal to a
> finite-number.
>

Alright the last post talking about how students learn the Peano
Axioms with its
Successor Axiom and how they are beguiled or mislead into a lifetime's
worth of
fakery. How they are mislead into thinking they have an infinite set,
whose individual
members are all finite-specimens.

And the trouble seems to lie with the fact that Peano did not use
Cauchy and the long
history before the Peano axioms concerning the theory of Series. That
if Peano had
simply used the theory of Series, he could not have thus clouded the
mathematics
world with the fakery of Successor as delivering only finite-
specimens. Now it is interesting
that a contemporary of Peano did not miss the opportunity to create
another system of
numbers whose axioms use the Cauchy Series, rather than some
convoluted Successor
function and that was Hensel with the p-adics.

So I am going to search through Cajori's book "History of Mathematics"
1991, to try to assemble the dates, rather than using Wikipedia which
would have few dates and be more gap
ridden since not one author wrote the entries. Cajori writes on page
373 " The faults of his time found their culmination in the
Combinatorial School in Germany, which has now passed into
oblivion."

What I am going to spy into is the idea that if Dedekind and Peano and
others had fixated on a
Series rather than a Successor function for the Natural Numbers, that
the Natural Numbers would be on the path of truth instead of their
path of disgrace and that the Cantor era going into
the Cohen Continuum farce would have never happened. As Cajori notes
of one case of
oblivion in the 1800s, it is my belief that if the Natural Numbers
Axioms had been based
strictly on Series would have caused Dedekind and Peano to also have
to define precisely
finite-number along with infinite-number and thus mathematics by the
1900s to 1990 would
have been a far more "cleaner and logical mathematics" rather than its
present day murky
and filled with fakery.

So let me follow some of that history, because the trouble I am seeing
is that for some reason,
Dedekind and Peano and others abandoned the Series and came up with a
screwy and wretched function of Successor, when their best path was to
have taken the Series and
made that the axiom of the Natural Numbers.

Also, one can argue that when Peano used the Successor as a function
and not as a purely
Series concept, that not only would that cover up the needed outcome
that the Natural Numbers have both finite-numbers and infinite-numbers
but that Peano, by using the Successor function is using the very idea
of Natural Numbers as counting, so that it is a
circular definition or circular axiom. In other words, Peano
incorporated into his Successor Axiom what the Natural Numbers are,
when it is the axiom that is supposed to create the
Natural Numbers. You see what I am saying, is that Peano had a
preconceived notion of
Natural Numbers and incorporated his preconception into the Successor
Axiom which
is verboten. A modern day analogy is that Svante Paabo is trying to
sequence the DNA of
Neanderthal and he is verboten to have impurity contamination into his
extracted Neanderthal
samples, such as the DNA from the modern humans of their hair or skin
falling into the
test samples of Neanderthal. So contamination is a vital concern in
Neanderthal DNA
sequencing. In like manner, when Peano devised a Successor function
for the axiom to
build the Natural Numbers, rather than just purely using Series of
endless adding of 1, that
Peano had contaminated the axioms with a preconceived notion of what
the Natural Numbers
already were, before creating the Natural Numbers. The Successor
function of Peano, has
the Natural Numbers already existing, and thus a erroneous set of
axioms.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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