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 2 years ago
1) Prove that if the sets ST and TS are equivalent, then S and T are equivalent.
2) Prove that
\[ sup\{r \in Q : r< \sqrt{5} \}=\sqrt{5} \]
 2 years ago
1) Prove that if the sets ST and TS are equivalent, then S and T are equivalent. 2) Prove that \[ sup\{r \in Q : r< \sqrt{5} \}=\sqrt{5} \]

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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0i am not sure what the first one means, but the idea for the second one is this: suppose by way of contradiction that the supremum is less than \(\sqrt{5}\) say it is \(\sqrt{5}\epsilon\) then since we know that between any two reals there is a rational, there exist some rational \(r\) with between \(\sqrt{5}\epsilon<r<\sqrt{5}\) contradicting the assumption that \(\sqrt{5}\epsilon\) is the supremum)

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0thank you satellite, this helped me a lot..
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