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The sequence sin(n) is bounded within [-1,1] , perhaps you mean n(sin(n)) which does not diverge to + or - infinity but oscillates between positive and negative, and increases in absolute value
Interesting function, kylekatarn. I've never thought of an unbounded sequence that had subsequences which one diverges to infinity and the other to negative infinity.
* it's not convergent (oscillates around y=0)
* it's not bounded (fully or partially):
* yet it doesn't diverge either to +oo or -oo because:
I'd agree with that. If it doesn't diverge to infinity then it has to be bounded by some number, even if it's a million or something.
oscillates: 1, -1, 1, -1, ...
But divergent not for -oo or +oo and unbounded, I am not seeing any example...
I have a question that says find an unbounded sequence that doesn't diverge to -∞ or ∞. I can't figure one out, I don't think it exists. Anyone know of one?