Thu, 27 Jun 2002 20:20:17 -0400 (EDT) "Wolf Kirchmeir" wrote:

It is much more complicated than what I am giving here below. But good
enough for every layman to get started on these ideas.

I called them the Infinite-Integers in 1991, and when I first posted
to the Internet circa 1993, I was pleased to find out that these
"infinite-integers"
already had a name and a strong background history starting with
Hensel.

Infinite Integers = p-adics unioned n-adics

The adics are base dependent and very difficult to explain to layman.

I like the clearcut and direct picture explanation of Infinite
Integers.

Take any Real number, flip it over, and then push all the numerals to
the left of the decimal point and you have an Infinite Integer.

Some Examples.

 Real Number 1.00000..... becomes Infinite Integer .....00000001.

 Real Number 5.3333...... becomes Infinite Integer .....33333335.

 Real Number 3.14159..... becomes Infinite Integer ......951413.

 Real Number 1000.101100111000.... becomes Infinite Integer
....0001110011010001.

 Real Number 999. becomes Infinite Integer ........000000999.

So you can get a sense of what p-adics are from these examples, only
it is far
more complicated.

What the big uproar that I have created in mathematics is that I have
said that the Finite Integers are a ill-defined set and an incomplete
set. That these finite-integers are really a tiny part of a larger set
which is the Infinite Integers. I have said that the Natural Numbers
are not just finite-integers but also the infinite-integers.

Natural Numbers = Finite Integers union the Infinite Integers.

By doing this, I eliminate all of the old Number theory problems that
have never been able to be proven. I wipe Number Theory clean and
conquer all of its problems by recognizing that the Natural Numbers
are a larger set then previously recognized.

If aliens came to Earth and said the Human species is a sperm cell.
Well, they would be minutely correct, but they neglect to see that the
human species is more than a sperm cell but a multicellular large
creature. Same thing as what happened in the history of mathematics,
in the failure to recognize that the finite-integers of 1,2,3,4,
....... eventually are the infinite-integers.

Both the Finite-Integers and Infinite-Integers (adics) are built from
one and the same axiom-- endlessly adding 1. Since they both are
manufactured from one and the same axiom, then, I argue they are one
and the same set of number.

The implications of this idea:

 Natural Numbers = finite-integers + infinite-integers (adics)

is revolutionary because it solves all of Number Theory, solves the
Cantor question of infinites, and solves other issues such as Riemann
Hypothesis and much more.