0^0

It is double valued;
0^0 = {0,1}
It is a special case of x^y. It looks like 0 from x, and like 1 from y.


Now consider measuring zero relative to itself;
0! / 0^0 = {1/1,1/0}
One value diverges, demonstrating that 0-base counting can not be done.
To overcome this measurement difficulty we break the symmetry of x^x
form to x^y form and then freeze x to its base. Taking the base as 2;
0! / 2^0 = 1/1 = 1
Then 0 acquires one state and enables measurement.

Obviously the base can not be 1. The next logical choice is 2. Boolean
is the minimum space.

.

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