Uniform continous functions?

Question

Please if someone could tell me how to show that $1\over x$ is not uniformly continuous on $(0,1)$.

I hope I've been clear enough, thanks.

Answer 1

It is continious on (0,1) but not uniform ontinious. Let $xn=1/(n+1/2)$ and $ yn=1(n-1/2) $f(x)=1/x. Let e>0.$|f(xn)- f(yn)|=1$, but for large enough n $|x_y-y_n|<e$. So $x_n$ and $y_n$ are close enough but $f(x_n)$ and $f(y_n)$are not.