Suppose and there is a such that . Show that .
I understand the definition of limit but I'm having trouble getting this proof started. Any help would be appreciated.
Oh, so a punctured ball...but then the claim is false: is such that
, and nevertheless ...
Note that , and I don't care if you want to puncture it and take the middle point out or not.
It's not hard to come up with a counterexample where f is continuous, so I think something must be missing in your question...or I misunderstood, of course.