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From: Archimedes Plutonium on 13 Feb 2010 03:16
So let us get a start on this project of defining the ellipsis in
Numbers from the precision
definition of finite-line and infinite-line in geometry. Those are the
line-segment with
two endpoints and the line-ray with one endpoint and a arrow
indicating an endless
string of points.

So the ellipsis in Numbers indicates an endless string of digits. So
that we can just
simply replace the ellipsis of four dots such as "...." with the arrow
of a line-ray of
----> So that when we write a number such as 1.9999.... we could
simply write it
as 1.9999 > indicating that in geometry it is endless points, and in
Numbers it is
endless string of digits.

Now can we use that arrow to show that infinity can be in the
midsection of a number
and where the number has a BackView and FrontView?

Take the interval on Reals of between 0 and 1.
0 .5 1
-----|---------------|-----

Now that shows the interval of 0 to 1 with 0.5 in the middle.

Now is there a number 0.99999......? Yes of course, only many in
mathematics
believes this number to be the same as 1 itself. Others, believe the
number
0.99999...... is the closest number to 1 but not equal to 1.

Here we can rewrite that number 0.9999...... such that we eliminate
the ellipsis
with a arrow, indicating an infinity of digits 0.99999> as if it were
a line-ray.

Now is there a number in that interval 0 to 1 that looks like this:

0.90000.....00500....0002

In old-math there can be only one ellipsis for a number and the above
would
have to be this: 0.90000..... or 9/10

So let us bring in geometry in full force and regalia.

Can we have in geometry a infinite-line with two arrows? Why yes of
course in that
the x-axis is just such an infinite-line of <----> where 0 point is
somewhere in there.

So why not have
0.90000.....00500 represented as 0.90000> <00500

and since we can add as many arrows as we wish without affecting
infinity,
that the number 0.90000.....00500....0002 in geometry would be the
infinite-line of 0.90000> <00500> <0002

In geometry the infinite line of <-----> is the same as <--<---->--->
or however
many other arrows you wish to tack onto. So in geometry when you have
an
arrow to infinity, you can tack on more arrows in that direction, and,
you can
pause to write out and show some finite string of digits and then
continue
onwards to the march of infinity.

Now in the pause to show a finite string of digits, matters not if you
pause in the
middle somewhere or pause at the ends, so long as there is a infinite-
interval of digits
of a Number or in the case of geometry, an infinity of points.

So in this reasoning, we can see that the definition of the arrow in
geometry for infinite-ray
or infinite-line is transfered to the definition of ellipsis in
Numbers. And the transfer shows that
the infinity can be in the midsection and demanding or forcing the
realization that a number
must have a Frontview and a BackView. In the case of geometry of the
interval 0 to 1,
we see that the 1 is not a digit of the number, nor is 0 the digit of
the number itself but that
the 0 and 1 of the interval serves as the FrontView at the 0 point and
the BackView of 1.

In other words, mathematics since the time of Pythagoras all the way
up to 2009, by never
defining finite-number with precision, suppressed and repressed the
correct and clear idea that
a number need not have just one solo singular ellipsis but can have
multiple ellipsis, just as
a infinite-line can have multiple arrows. And that the precision
definition of finite-number
given by the use of a proof from geometry, that a Selection was made
such as 10^500,
that all numbers have a FrontView as well as a BackView.

And only the present day, repressive and suppressive math community
has kept that information out of the public awareness. A community
that cannot admit they never had
a precision definition of "finite-number". A community that acts
clownish when someone
gives them a number like 9999.....9999 and where they clownishly say
they do not understand
what the ellipsis is or that the BackView is "un math". Well, their
clown act can only last for a
short time, before reason steps in. Before people with reason asks the
members of the math
community for their precision definition of finite number. And since
no-one in the math community from Pythagoras to 2009 has ever given a
precision definition of finite-number,
we can laugh at the present day clowns of the math community.

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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