So another easy question. The title is Theorem (1.17) from Stromberg part (iii). I know there are easier arguments to prove this, but I would like to understand the author's reasoning.
To prove (iii) he uses induction. For the basis step, if $n=1$ and $x+n\in\mathbb{N}$, then by (ii) [already proved] $x+1-1\in\mathbb{N}$, or $x\in\mathbb{N}$. Why it is so obvious from this statement that $x=1$? (It could well be 2,3,etc.)