Gödel Without Tears -- 5

Here now is the fifth episode on the idea of a primitive recursive function. The preamble explains why this matters and where this is going. [As always, I'll be very glad to hear about typos/thinkos.]

The previous episodes are available:

1. Episode 1, Incompleteness -- the very idea (version of Oct. 16)
2. Episode 2. Incompleteness and undecidability (version of Oct. 26)
3. Episode 3. Two weak arithmetics (version of Nov. 1)
4. Episode 4. First-order Peano Arithmetic (version of Nov. 1)