Whence function notation?

I begin — in continental style, unmotivated and, frankly, gratuitously — by defining Ackerman’s function \(A\) over two integers: \[ A(m, n) = \left\{ \begin{array}{l} n + 1 & \mbox{ if $m=0$ } \\ A(m-1, 1) & \mbox{ if $m > 0$ and $n = 0$ } \\ A(m-1, A(m, n-1)) & \mbox{ if $m […]