Unformatted text preview: the set of positive integers is not bounded above. Furthermore, use this result to prove that for any , there is some positive integer n such that . 2. Prove that for real numbers with , then there is a rational number x such that . 3. Verify with an proof that 4. Suppose and for all n . Prove directly that if and are Cauchy, then is also Cauchy. 5. For each positive integer n , set Prove that . You may use the fact that the sum of the first n positive integers is 6. Prove the Cauchy Criterion: A sequence converges if and only if it is Cauchy....
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 Spring '08
 PLOTKIN
 Math, positive integer, Cauchy, Cauchy criterion

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