P-007 A powerful paradox!

Consider an infinite tower of powers of x:

Y = x^(x^(x^(x …

‘^’ is the exponentiation operator.

The equation Y = 2 can be solved by noting that Y = x^Y, so that 2 = x^2, or x = sqrt(2).

But then, if Y = 4, we can similarly solve for 4 = x^4, giving 2 = x^2 again. So the question is, what is the value of Y when x = sqrt(2)?

In general, what is Y(x)?

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