(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex] A = \left\{(x,y): 0\leq xy \leq 1\right\}, A \in R^{2} [/tex]

I'm trying to determine if this set is bounded and/or closed.

2. Relevant equations

if X = (x,y)

euclidean metric: [tex] ||X|| = \sqrt{x^{2}+y^{2}} [/tex]

3. The attempt at a solution

I know a bounded set => ||X|| [tex] \leq [/tex] k

so I need to show somehow

[tex] ||X|| = \sqrt{x^{2}+y^{2}} \leq k [/tex] (somehow)

and closed => every limit point belongs to the set. So take an arbitrary X'= (x',y') [tex] \in [/tex] A'. Then there exists X_{n}= (x,y) [tex] \in [/tex] A such that X_{n}-> X' and X_{n}[tex]\neq[/tex] X'.

X_{n}[tex] \in [/tex] A => [tex] 0 \leq xy \leq 1 [/tex]

Need to show X' is such that [tex] 0 \leq x'y' \leq 1 [/tex] (somehow)

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# Closed and bounded

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