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Logical tetration equation - Xorter - 02/01/2018

Let us define analytic or function like this way:

x or y = lim(h->infinity) bitor(floor(x*2^h),floor(y*2^h))/2^h;

Now, here is for instance two functions:
f(x) = x^x = x^^2;
g(x) = x or x^x;

The equation:
f(x) = g(x)

What is the solution set?