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(BTW in rereading my comments above I come off as fairly obnoxious. That wasn't my intention, so please accept my apologies.)
And one last comment... I think I will change the definition of the set of p.r. functions to an inductive one rather than using terms like "smallest" and "closed", as upon further study, the latter, taken in the set-theoretic sense, presupposes infinite classes of functions, whereas with the former we can stay safely away from the i- word. --[[User:Wmorgan|Wmorgan]]
You need at least the Peano axioms; otherwise you cannot talk about natural numbers in any meaningful way. I would probably not even bother; just mention the natural numbers, link to them, and be done with it. Then later show that the "intuitive addition" of natural numbers can be defined as a p.r. function. Everybody knows the natural numbers (or they think they do).
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