Intelligent Infinity Defined

[tadeus]

Having several infinities as in ordinary math might be more practical than dealing with potential infinities. One idea I came to think of is to have sizes of potential infinities based on the size of all natural numbers 0, 1, 2, 3, 4, 5, ... as the unit size U. So for example all even numbers 0, 2, 4, ... have the size 0.5 U. And all odd numbers 1, 3, 5, ... also have the size 0.5 U. And then all natural numbers 1 U = 0.5 U + 0.5 U.

O.K. Why not.
When this definition is helpful it is a good definition.
It's not different to the definition of imaginary numbers with i² = -1