Suppose $f$ and $g$ are functions from $\mathbb N^+$ to itself. I want to consider the function $f^g$, where $f^g(n) = f \circ \dots \circ f(n)$, where composition is done $g(n)$-many times. Note that if $f$ and $g$ are monotonic increasing then so is $f^g$. Is there a name for this operation, or something similar?
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asked Oct 7, 2019 at 17:09
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1$\begingroup$ That would be $n\mapsto(\ulcorner g(n) \urcorner\, f) (n)$, where $\ulcorner m \urcorner$ is the Church numeral for $m$. $\endgroup$– Pedro Sánchez TerrafCommented Oct 8, 2019 at 12:35
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