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Math Help - upper and lower bounds of a set with two variables

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    upper and lower bounds of a set with two variables

    I have a problem with writing a decent proof on upper and lower bounds
    of two sets - A={\frac{n-k^{2}}{n^{2}+k^{3}} ,  n,k \in \mathbb{N}} and  B={\frac{m^{2}-n}{m^{2}+n^{2}} ,  n,m \in \mathbb{N}, m>n} .


    I don't know how to cope with these two variables. I want to prove the
    upper and lower bounds (for B supremum = 1 and infimum =1/2) using the
    definition. I assume that for the supremum of B  \epsilon>0 and
     \frac{m^{2}-n}{m^{2}+n^{2}} >\epsilon and I want to show that for all n>n_\epsilon . How can I do it?
    Last edited by Lisa91; November 11th 2012 at 05:31 PM.
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