I am trying to get a good understanding of the concepts of lim sup, lim inf and oscillation of a function. I am lacking a source of good examples of these concepts. Can anyone advise me of a text or web site that provides some actual examples of finding lim sup, lim inf and oscillation (at a point) of a function.

A particular problem.

I wish to rigorously prove the following statement from Wikipedia regarding the oscillation of a function:

.sin (1/x) has oscillation 2 at x = 0, and 0 elsewhere

Can anyone help with a proof to give me an idea of the method for rigourously establishing the oscillation in the above case..

Bernhard