hello ,
im having trouble with proving sqrt(n) is not cauchy.
Please help.
Alternatively give me any $\displaystyle \epsilon>0$ and N>1, then find an $\displaystyle n>\epsilon$ with n>N (natural numbers are unbounded). Then $\displaystyle n^4>n^2>N$ and moreover
$\displaystyle |\sqrt{n^4}-\sqrt{n^2}|=|n^2-n|=|n(n-1)| \geq n > \epsilon$.