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Unformatted text preview: has no rational least upper bound. 4. Verify with an proof that 5. We say a sequence is almost Cauchy or pseudo-Cauchy if for every , there is some positive integer N such that for all , . Is it true that every pseudo-Cauchy sequence is convergent? If so, prove it. If not, provide a counterexample. Is it true that every convergent sequence is pseudo-Cauchy? If so, prove it. If not, provide a counterexample. 6. Let S be nonempty set of real numbers that is bounded above. Let . If , prove that there exists a sequence of terms completely in S such that for each index n ....
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This note was uploaded on 12/13/2011 for the course MATH 115 taught by Professor Plotkin during the Spring '08 term at Rutgers.
- Spring '08