I looked at your answer to the question posted How to prove $\sin(1/x)$ is not uniformly continuous
thank you for your helpful explanation on how to think about it. But I am failing to see why we will choose $x=\frac{1}{2πk−π/2}$ . I know that we want something $\sin(1/x)=1$ and $\sin(1/y)=−1$, but how did you get that answer. Would you mind elucidating on your motivation?
Also, I am struggling to get an intuitive idea to work with continuous uniform problems. I understand the definition, but am failing to work with it.
Thanks