Thread: Show a function is continuous at every point in Reals

Let K be greater than 0 and let f : Real numbers --> Real numbers satisfy the condition |f(x)-f(y)| less than or equal to K|x-y| for all x, y in Reals.
Show that f is continuous at every point in c in Reals.
Thank you.

Originally Posted by gixxer998

Let K be greater than 0 and let f : Real numbers --> Real numbers satisfy the condition |f(x)-f(y)| less than or equal to K|x-y| for all x, y in Reals.
Show that f is continuous at every point in c in Reals.

Originally Posted by Plato

Thank you. How did you come up with this?

that's Lipschitz condition, and every Lipschitz function is uniformly continuous, hence continuous.

Plato is telling you to pick that to show the uniform continuity.