f is a continuous function in such as:
I showed that , but idon't know how to deduct that
f is constant????
This is obviously just a corollary of a much larger theorem.
Theorem: Let be a continuous function such that for all . Then, .
Proof: First suppose that and define a sequence as and . Clearly then , and thus . It is also clear that . Thus, the last part gotten from continuity since for continuous .
The conclusion follows