i look every where for that basic proof
lim inf An=lim sup An then the sequence converges
That is how I would do it. Is that acceptable?
You may find this thread helpful http://www.mathhelpforum.com/math-he...-analysis.html
I'm not quite sure what you mean by this? Do you mean the f maps to a single value kind of constant or some other kind...either way I don't think I assumed anythingsecondly, your proof suggests that the sequence is constant, which of course, is not true for convergent sequences in general.