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From: Archimedes Plutonium on 17 Jan 2010 15:26


Archimedes Plutonium wrote:
> Alright, most people who are in math or dabble in math are going to
> "shut-up" once
> asked to define precisely what is a "finite number versus an infinite-
> number".
> Occasionally, some misguided person is going to belch out "finite-set"
> not knowing
> that we are talking about numbers, not sets. And even so, if we saddle
> numbers
> with a set-theory definition derived from finite-set and infinite-set
> we have
> counterexamples to show them that set-theory is flawed.
>
> So I asked : Nam Nguyen for his most precise definition of "finite
> number" and he seems to have run away into hiding. I have asked Peter
> Nyikos for his best precise definition
> of "finite-number" and he seems to have run away into hiding. I have
> asked David Bernier for his best precise definition of "finite number"
> and no reply.
>
> So, I can take this survey right to sci.math itself, and without
> having to ask anyone who
> posted to sci.math of its entire history of posts, I can conduct a
> survey to see how many
> people understand and accept the definition of "finite-number versus
> infinite-number"
> as being the definition: a finite-number repeats in an endless string
> of zeroes leftward
> so that 9999 is finite because it is .....00009999 whilst 9999....9999
> is infinite. The immediate
> contradiction of such a definition is that what about a number such as
> 00009999....999
> which is finite according to that definition.

Sorry, typing too fast, for that should have read 0000....9999. The
idea is that when finite-number is defined in this manner
we leave it open as to ambiguity and confusion and so it cannot be a
precise
definition of "finite-number". And this is what I mean that
the only precision definition is to come down hard and select a number
and
call it the boundary mark of Finite and beyond is infinite (and to
sandwich a
Incognitum between Finite and Infinite).

>
> So to conduct a survey of all of sci.math as to how many people have
> accepted and endorse
> that definition of finite-number is very easy to conduct, because the
> Reals of mathematics
> is defined as a finite-string leftwards of the decimal point with a
> infinite string rightwards.
> So in other words, everyone who accepted the definition of a Real
> Number has tacitly assumed that a finite-number is a number that ends
> in a repeating string of zeroes leftwards.
>
> So even if Nam Nguyen and Peter Nyikos and David Bernier run away and
> hide from my question of them defining precisely finite-number versus
> infinite-number, because they
> accept and use the Reals is admission that they accept the definition
> of finite-number
> as being a number that ends in an infinite string of zeroes leftwards.
>
> Now if I go through sci.math, I will actually see some posts in which
> people have said
> Reals are finite strings leftward of the decimal point. This is
> tantamount to saying
> Reals are finite-numbers left of the decimal point because they repeat
> in zeroes to infinity.
>
> This is the reason why ten professors of prestigous colleges on the
> East Coast said that
> a finite-number is ending in zeroes leftwards, because they were
> simply repeating what
> they believed was the accepted definition of a Real Number.
>
> Now we can dive into the definition of Series and to make clear what
> we mean by a
> "string of digits". In that the Series 1 + 1 +1 +1 + . . . . + 1 is
> seen as the Successor
> Axiom of Peano axioms and it ends up being an infinite number since it
> is unbounded.
> Now the old-math could never represent that number other than a
> sideways 8 as indicating
> infinity, but with the FrontView and BackView of numbers I can easily
> say that in decimal
> number representation that series of adding 1s endlessly equals the
> number 9999....9999,
> or in binary is equal to 1111....11111. So how we define "string of
> digits" in mathematics?
> Well we use the Series definition that a String of Digits is either
> the leftward portion of
> a Real-number from the decimal or the rightward portion of a Real
> Number from the decimal
> point. So that we can say a Finite-Number is a string that ends in
> zeroes to infinity.
>
> So how does Series define a finite-number such as "6"? Well it be like
> this:
> 1 + 1 + 1 + 1 + 1 + 1 + 0 + 0 + 0 + ....+ 0
>
> So, enough of a preliminary, now we can conduct a full survey of
> Sci.math going back
> further than the year 1993. My history of sci.math goes back only to
> August of 1993, but
> sci.math goes back further. And we can inspect any post by anyone who
> talks about
> finite versus infinite and who talks about Real-numbers.
>
> And in fact we can include everyone who wrote a mathematics textbook
> to figure out
> if the author had it in mind that the meaning or definition of "finite-
> number" was a
> definition revolving around the idea of string of zeroes leftwards to
> infinity.
>
> So, Nam, and Peter, and David, you probably do not have to waste your
> time with what
> you believe is a finite-number, because you probably already displayed
> your understanding
> of what that definition is for you by the simple full endorsement of
> what a Real-Number is.
>
> You see, I vary from every one else as to what is a Finite-number and
> thus what is a
> valid-Real-Number. The Real Numbers ends at 10^500 since that is the
> end of finite-number
> and thus algebra on Reals ends at 10^500.
>
> So a survey of everyone who posted to sci.math and to everyone who
> wrote a book on
> mathematics and who endorsed the Real-Numbers, everyone of them
> accepted, whether
> they realized it or not realized it, they accepted the definition of
> finite-number as being a
> number in which the leftwards string of digits eventually ends in
> nothing but zeroes.
>
> All of those people assumed what finite-number was, and that is the
> reason mathematics
> starting with the Peano Axioms are inconsistent and that mathematics
> as a whole is
> in a dreadful state of collapse. When mathematics fails to precisely
> define its concepts,
> it fails to live up to its primary job-- precision, precision,
> precision. The reason Goldbach
> Conjecture or Fermat's Last Theorem or Riemann Hypothesis or Perfect
> Numbers Conjecture
> could not and will never be proven is because we never defined finite-
> number with precision.
> We assumed what finite-number meant.
>
>
> 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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