This confused me,
$\lim_{n \to \infty} x^{1 + \frac{1}{2n-1}} = x \lim_{n \to \infty}x^{\frac{1}{2n-1}}=|x| $
Which means $\lim_{n \to \infty}x^{\frac{1}{n}} = \left\{ \begin{array}{lr} 1 & : x > 0\\ -1 & : x < 0\\ 0 & : x = 0 \end{array} \right.$
Rudin gives an easy proof as to why this works when x is nonnegative, but when x is negative I don't know how to deal with fractional powers of negative numbers. Is this something I simply can't do without further reading or am I being stupid?