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Suppose the iterative root of ##2^x## :

##\phi(\phi(x))=2^x## (I suppose the Kneser calculation should work, it affirms that there is a real analytic solution)

Then how to compute ##\phi(\aleph_0)## ? (We know that ##2^{\aleph_0}=\aleph_1##).

Could this be ##\aleph_{1/2}## ?