sorry for this basic question but I was just going through Rudin's Principles textbook, and it says in theorem 1.21 (p.10):
$\textit{For every real $x>0$ and every integer $n>0$ there is one and only one real $y$ such that $y^n=x$}$
But what about $x=4$, $n=2$? Then both $y=2$ and $y=-2$ satisfy the relation, no?
Thx a lot for any help on interpreting this!
You are right the theorem is stated incorrectly . The theorem does however hold if one adds the condition that $y>0$ .