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?
"Divergent" means "not convergent"... there are "oscillating" sequences that don't converge, like this one:
But divergent not for -oo or +oo and unbounded, I am not seeing any example...
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.
Why did the vector cross the road?
It wanted to be normal.
but what can we say about:
* it's not convergent (oscillates around y=0)
* it's not bounded (fully or partially):
Last edited by kylekatarn (2007-02-13 03:48:02)
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.
As for mine, I always stick with trig:
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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