Hypothesis/Conjecture = Any set can be mapped to any other.

I will start by prooving the set of rational numbers |R| can be mapped to the set of natural numbers |N|.

So...

|R|=|N|=ℵ0

So to start, lets assume all rational numbers can be expressed as fractions or decimal numbers,
now lets assume a set of all numbers and fractions will also contain all of these fractions and decimal numbers
So once we show this set of all numbers and fractions can be mapped to the natural number set,
and that no new number outside of it can be created
it will be apperent that these sets are the same.
only differing in the meaning we project onto them.