Creation of complex numbers
Expansion by inversion
Creation of fractions
Creation of negative numbers
By the same scheme, transform
is a natural number), if applied to natural numbers, leads to negative integers.
Consider the set of natural numbers
Find the image of the set under the transform
Set of images is
The set of images is naturally complemented to the set
of all natural numbers:
Now apply the inverse transform
to the complemented set
We arrive at new numbers: These are new negative numbers.