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**Borkborkmath** "Let I be the set of real numbers that are greater than 0. For each x$\displaystyle \in$I, let $\displaystyle A_x$ be the open interval (0,x). Prove that $\displaystyle \cap$$\displaystyle _{x\in I}$$\displaystyle A_x$ = $\displaystyle \emptyset$, $\displaystyle \cup$$\displaystyle _{x\in I}$$\displaystyle A_x$ = I. For each x $\displaystyle \in$ I, let $\displaystyle B_x$ be the closed interval [o, x]. Prove that $\displaystyle \cap$$\displaystyle _{x\in I}$$\displaystyle B_x$ = {0}, $\displaystyle \cup$$\displaystyle _{x\in I}$$\displaystyle B_x$ = I$\displaystyle \cup${0}."