Also I do believe the real and natural number sets have cardinality, its just complicated to demonstrate.

Eg. You give me 0.1, I give you 1, you give me 0.2, u give you 2. Now you yet to get clever and give me 0.15, I give you 3. You give me 0.15789, I give you 4. You can go on to infinity, interestingly enough, so can I.