Unique Solution Exists to x^n=y: Real Analysis Proof

[imranq]

Homework Statement

Given x > 0 and $$n \in N$$, prove that there is a unique y > 0 s.t. $$y^n = x$$ exists and is unique

Homework Equations

Hint is given: consider $$y = 1. u.b. \{s \in R : s^n < x\}$$

The Attempt at a Solution

I'm not used to this style of proof (real analysis I), help would be appreciated, thanks. BTW, what does "u.b." signify?

 

[Dick]

It's actually l.u.b. with a letter "L" instead of a digit "1". It means "least upper bound. Does that help?

 

[imranq]

oh, now its clearer. thanks