Existence_Uniqueness_Positive_Root

Let $x \in \R$ be a real number such that $x \ge 0$. Let $n \in \Z$ be an integer such that $n \ne 0$. Then there always exists a unique $y \in \R: \paren {y \ge 0} \land \paren {y^n = x}$. Hence the justification for the terminology '''the positive $n$th root of $x$''' and the notation $x^{1/n}$.