Notations:
ssrt(x) = \sqrt {x}_s (Super Square Root).
x^^(1/2) = ^{\frac 12}x (half fractional tetrations).
Does \sqrt {x}_s = ^{\frac 12}x?
Actually no.
because that means
If a = ^{b}n then n = ^{\frac 1b}a
Let us assume that is true.
if ^{n}x = z , n aproaches to infinity.
Then x = ^{\frac 1n}z= ^{0}z
As a fact, we already know that
^{0}z is always equal to 1.
but x = z^{\frac 1z}.
Hence the result is ^{0}z = ^{\frac 1z}z and that is not true.
Therefore the assumption has failed.
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