Prev: modal logic exercise
Next: sci.math-survey and math textbook survey of defining "finite number" #308; Correcting Math
From: Archimedes Plutonium on 17 Jan 2010 14:58
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.

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
From: David R Tribble on 18 Jan 2010 22:57
Archimedes Plutonium wrote:
> 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.

I'm curious about that survey you did in 1991. Did any of the
professors mention a book or two where this definition of
"infinite left strings of zero digits" can be found?

I've read a small stack of math books, but I've never seen a
definition like that in any of them.

Or perhaps there is a name associated with that definition,
like there are names attached to almost every other theorem
in math?

And for the record, it's pretty easy to provide an understandable
definition of "finite number" without having to mention sets.
 | 
Pages: 1
Prev: modal logic exercise
Next: sci.math-survey and math textbook survey of defining "finite number" #308; Correcting Math