Let r be a rational number greater than 1 and let f:R --> R be a function that satisfies abs(f(y)-f(x)) is less than or equal to (y-x)^r for all x, y in R. Prove that f is continuous on R.
Let r be a rational number greater than 1 and let f:R --> R be a function that satisfies abs(f(y)-f(x)) is less than or equal to (y-x)^r for all x, y in R. Prove that f is continuous on R.
Apply the very definition of continuity taking, for any $\displaystyle \epsilon>0\,,\,\,\delta=\sqrt [r]{\epsilon}$