I am trying to understand what they are doing here to demonstrate instability:
I know that to demonstrate that this process is unstable, I must take a sequence $\{x_n(t)\}_n$ such that $x_n(t)\to x(t)$ and see that the corresponding output values $\{y_n(s)\}_n, 0\leq s\leq 1$ converge not to $y(s), 0\leq s\leq 1$, but in this example do the opposite or is it my opinion. Could someone explain to me please?