# Analysis problem

1. Jan 26, 2010

### imranq

1. The problem statement, all variables and given/known data
Given x > 0 and $$n \in N$$, prove that there is a unique y > 0 s.t. $$y^n = x$$ exists and is unique

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

3. 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?

2. Jan 26, 2010

### Dick

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

3. Jan 27, 2010

### imranq

oh, now its clearer. thanks