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From: Archimedes Plutonium on 25 Jan 2010 00:33


Brian wrote:
> You have the number of ways q quanta can be arranged. Next you have
> the number of ways of arranging these arrangements. Continue long
> enough and you'll eventually surpass the "largest number" in finitely
> many steps.
>

Well, Brian, mathematics first job is to define precisely what finite-
number is.
Math has failed to do that and as a consequence we have thousands of
unsolved
and unsolvable problems in mathematics number theory. Not because they
are
difficult problems, but only because the concept of finite-number is
crucial to those
problems and yet finite-number is ill-conceived.

Example: in geometry we define the rectangle with precision for
Euclidean geometry,
and as a consequence there is no backlog of unsolved problems
concerning rectangles
in Euclidean geometry. Why is that? Because we have a precision
definition.

Now look at mathematics Number theory and there sits the worlds oldest
unsolved
problem going back to Ancient ancient Greeks of the perfect numbers
conjecture. It
is a simple to understand problem and there is nothing in any of the
other sciences that
even remotely resembles the unsolvability of Perfect Numbers. Now most
everyone in
the world including you, probably, thinks that Perfect Numbers is just
a tremendously
hard problem. But I think the truth of the matter is that because
finite-number was
never well-defined, never given a precision definition, that Perfect
Numbers could never
and will never be proven.

Now, let us say tomorrow we define Finite Number precisely as 10^500
or below
and beyond is Infinite-numbers. Then in a weeks time, we can check
through all those
numbers and announce that Perfect Numbers was proven true.

You see, when math has trainloads of murky defined concepts gives rise
to unsolved
and unsolvable problems. Finite Number is math's most horribly defined
concept and that
is why math has to reach back to Ancient Greeks with still Perfect
Numbers open. Physics
nor chemistry, nor biology, nor geology, nor astronomy nor medicine
nor any other science
has to reach back to Ancient Greeks for solving some problem started
there. Because all of those sciences have made more precise
definitions of their concepts than the Ancient Greeks
ever dreamed about. However, math, the only science at present day,
still has to go back to
Ancient Greeks to try to solve the Perfect Numbers.

So, Brian, do you really think that the concept of finite-number was
ever given a precision
definition?


> This might prove useful to your investigation :
> http://en.wikipedia.org/wiki/Finite_set
>

Finite-number, not finite set. Numbers and sets are independent in
this topic
just as if I were talking about a precision definition of finite-line,
I would not
look for set theory to render a definition of finite-line. To define a
finite-line from
an infinite-line I would do the same as with numbers. I would look to
Physics
for the largest number possible in Physics which is the Couloumb
Interactions
of element 109 of a number about 10^500. So I would define a finite-
line as
all lines of that number or less and any above that number are
infinite lines.
I could have a Incognitum region of lines sandwiched in between finite
and infinite.

Now whether you like that or not Brian that is a **precision**
definition for there
are never any doubt as to whether a line is finite or infinite. Now
you may ask is that
10^500 cm or meters or kilometers or what. And I would answer you that
in Physics
there is no need for any number beyond 10^500 in any physical physics
measurement
or experiment so it does not matter whether you want kilometers or
millimeters. If I
remember correctly the Planck Unit for distance is very far below
10^500.

The point is Brian-- precision precision precision and when you say
10^500 you have
fulfilled the precision task.

> Descriptors in mathematics may not be how those descriptors are used
> outside of mathematics. As an example, a number is called "rational"
> iff certain criteria are met. However, outside of mathematics, if
> someone is irrational, then they are in some way psychologically
> unstable. Assuming that numbers don't possess minds of their own, a
> rational number does not literally mean it is psychologically stable/
> healthy.
>

Precision definition is far more of a task than your mere ideas of
descriptions.

Precision definition eliminates ambiguity and confusion.

Is the number 0000.....99999 a finite-number or a infinite-number?
According to
present day mathematics, noone knows. Noone in the math community has
a definition
of finite-number to decide, except me, who says that 10^500 is finite
and that number
is thus infinite-number. But everyone else in the math community must
admit that
0000....99999 is a finite number since it ends in zeroes to the
leftward of the string
just as 99 is finite because it is 000000.....0099

So we are talking about precision, not loose descriptions.


> Mathematical descriptors are not compelled to coincide with either
> intuition or how those descriptors are used in the natural language.
>
> The example at hand is the descriptor 'finite'.
>
> The intuition on the word is that if you have a group of marbles and
> if there is a basket big enough to hold them, then that group is
> finite.
>
> We might as well classify numbers as Type I and Type II where Type II
> would be the property "not Type I."
>
> Using these generic descriptors, we can move past the baggage
> associated the word 'finite'

Oh, so you are saying much of what Peter Nyikos says that finite-
number
is a intuit like that of "time or space".

Well, math primary job is precision and not your foggy intuition or
descriptions.
Math did a precision on defining rectangle or square or circle or
tangent or
prime number or derivative or integral.

So why become derelict and lazy about a precision definition of finite-
number.


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: Nam Nguyen on 25 Jan 2010 01:07
Archimedes Plutonium wrote:
>
> Brian wrote:
>> You have the number of ways q quanta can be arranged. Next you have
>> the number of ways of arranging these arrangements. Continue long
>> enough and you'll eventually surpass the "largest number" in finitely
>> many steps.
>>
>
> Well, Brian, mathematics first job is to define precisely what finite-
> number is.

Well, AP, the last time one look a (making-sense) definition has existed.

> Well, math primary job is precision and not your foggy intuition or
> descriptions.

No kidding. But you forgot that a a mathematical definition *must* also
make mathematical sense. If I define a finite number as one no greater than
1, would that make sense.

Similarly, your definition of a finite number as one no greater than 10^500
doesn't mathematically make sense.

> Math did a precision on defining rectangle or square or circle or
> tangent or prime number or derivative or integral.

OK.

>
> So why become derelict and lazy about a precision definition of finite-
> number.

It's you who's derelict and lazy to learn that one can easily come up
with a sound definition of a finite number, and that there have *actually*
been more than 1 or 2 ways of defining it!
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