In Terence Tao "Analysis", the definition of the addition of natural numbers refers to a previous definition of $m+n$, but I can't find it.

Question

Has anyone read about Terence Tao's Analysis?

Definiton 2.2.1 Addition of natural numbers

... " From our discussion of recursion in the previous section, we see that we have defined $n + m$ for every natural number $n$. Here we are specializing the previous general discussion to the setting where $a_n$ = $n+m$ and $f_n(a_n) = a_n++$. "

I can't find the definition section about $n+m$ in the previous section, can anyone tell me where this definition is?

Answer 1

From our discussion of recursion in the previous section, we see that we have defined n+m for every natural number n.

This doesn't say that we have defined $n+m$ in the previous section. It says that we have discussed recursion in the previous section - right before the proposition 2.1.16. And it claims that we can apply that discussion to define the addition of natural numbers recursively.