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Increasing Sequence

  • Thread starter Icebreaker
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  • #1
Icebreaker
Suppose f:[a,b)->R is such that lim(x->b-)=+inf. Prove that there exists an increasing sequence {x_n} in (a,b) such that f(x_n)>n for all n.

I don't know where to start. It would be easy if I can prove that f is strictly increasing after some point. f might not be continuous so I can't simply look for all f(x) in the form x^2 or something... Too many possibilities. Any pointers will be helpful!
 
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  • #2
benorin
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What do you have for a definition of lim(x->b-)=+inf ? This will tell you where to start.
 

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