The following question was part of my analysis assignment and I was unable to correctly solve it.
Is $\sin(1/x)$ uniformly continuous on $(0,1)$?
The following reasoning was given by my instructor : Is $\sin(1/x)$ can't be continuously extended to $0$. So, its not uniformly continuous on $(0,1)$.
But I have a question : why we need to extend Is $\sin(1/x)$ continuously to $0$ when asked domain is $(0,1)$?
I am not satisfied by the reasoning of my instrictor.
So, I am looking for a rigorious explanation here.
Thank you!!