(where is a natural number), if applied to natural numbers, leads to negative integers.

**Original set:**Consider the set of natural numbers

**Image:**Find the image of the set under the transform

Set of images is

**Complement:**The set of images is naturally complemented to the set of all natural numbers:

**Inverse Transform:**Now apply the inverse transform

to the complemented set of images-
**Negative Numbers!**We arrive at new numbers: These are new negative numbers.