Let f be a real-valued function with dom (f) Subsetequalto R. Prove that the following are equivalent: (i) f is continuous at x_0 (ii) for every monotonic sequence x_n in dom(f) that converges to x_0, we have lim f(x_n) = f(x_0).
Show transcribed image textLet f be a real-valued function with dom (f) Subsetequalto R. Prove that the following are equivalent: (i) f is continuous at x_0 (ii) for every monotonic sequence x_n in dom(f) that converges to x_0, we have lim f(x_n) = f(x_0).