I was doing an exercise in a book which asked the question "what can be said about a divergent sequence which diverges to neither $\infty$ or $-\infty$?" I came up with the answer that it is bounded. I was wondering two things:
1. Is there anything more you can say about it?
The above led me to think about:
2. Is there a concept of a sequence of numbers converging to a certain range of numbers? and would this even be useful? I'm thinking then that the $\epsilon, N$ defn. of convergence to a limit would be a special case of the "convergence to a range of numbers" when the range has only one number in it.
Thanks for any thoughts/advice. :)
p.s. the exercise is not for a grade for a class, it's just out of curiosity.