(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

Find the infimum and supremum of each of the following sets; state whether the infimum and supremum belong to the set E.

[tex]

\item 1. ~~~~E={p/q \in \mathbf{Q} | p^2 < 5q^2 \mbox{ and } p,q >0}. \mbox{ Prove your result. }

\item 2. ~~~~E={2-(-1)^n/n^2|n \in \mathbf{N}. \mbox { Just list your answers}.

[/tex]

2. Relevant equations

[tex]sup E - \epsilon < a \leq sup E.[/tex]

3. The attempt at a solution

[tex]

\item 1. ~~~~ \mbox{Here I claim the supremum of E is }\frac{1}{\sqrt{5}}, \mbox{ in E, and the infimum of E is 0, which is not in Q}.

\item \mbox{Proof: Assume p, q greater than 0. Then } p^2 < 5q^2 \Leftrightarrow p < \sqrt{5} q \Leftrightarrow s = sup E = p/q = \frac{1}{\sqrt{5}} \mbox{how do I prove the infimum part. Hmm...}

\item 2. ~~~~ \mbox{inf E = 0, sup E = 2 (assume 0 in N). }

[/tex]

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# Homework Help: Infimim and supremum proof

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