Consider the transform of the set of natural numbers

(called the

The set of images (transforms) is the set of even numbers:

**
Complement**

The set of images (even numbers) is
naturally complemented to the set
of
all natural numbers:

** Inverse Transform**

Now apply the inverse transform

to the complemented set of images

Notice that the solution does not exist if only integers are considered. New objects - fractions - are introduced to resolve the contradiction.

We arrive at new (``super'' natural) numbers: These are the simplest fractions