All Questions
2
questions
0
votes
0
answers
70
views
Proving the uniqueness of x=sqrt(r)
Given any $r \in \mathbb{R}_{>0}$, the number $\sqrt{r}$ is unique in the sense that, if $x$ is a positive real number such that $x^2 = r$, then $x = \sqrt{r}$
I would appreciate any nudge in the ...
3
votes
4
answers
941
views
Why does a/b have to be in simplest form in the proof of irrationality for sqrt2
The proof of the irrationality of $\sqrt{2}$ starts with the supposition that $\sqrt{2} = \frac ab$ where $a$ and $b$ are integers. I understand that, but why is it important that $\frac ab$ is ...
- 31