Church ends up defining zero as the identity function, and N as "apply a function to a zero-unit N times"<p>While defining numbers in terms of their successors is decently doable, this logical jump (that works super well all things considered!) to making numbers take _both_ the successor _and_ the zero just feels like a great idea, and it's a shame to me that the papers I read from Church didn't intuit how to get there.<p>After the fact, with all the CS reflexes we have, it might be ... easier to reach this definition if you start off "knowing" you could implement everything using just functions and with some idea of not having access to a zero, but even then I think most people would expect these objects to be some sort of structure rather than a process.<p>There is, of course, the other possibility which is just that I, personally, lack imagination and am not as smart as Alonzo Church. That's why I want to know the thought process!