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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- Spring '08
- Math, Rational number, Cauchy sequence, convergent sequence