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Define $N_n$ as $n$ th natural number: $N_0=0, N_1=1, N_2=2, ...$. What happens after exponentiation? We have the following equation: $2^{N_n}=N_{2^{n}}$. (Which says: For all finite cardinal $n$ ...

This is a follow up to Will Brian's answer to this recent question. In particular, quoting Brian: "In fact, Paul Larson has pointed out to me that the statement "$\phi$ and $\phi^{-1}$ are conjugate"...