Prafull Kumar Mehta posted an Question
August 09, 2020 • 06:07 am 30 points
  • IIT JAM
  • Mathematics (MA)

Prove that cauchy sequence of real numbers is bounded.

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  • Shashi ranjan sinha

    see the attachment. Every Cauchy sequence of real numbers is convergent (proof given in attachment) and bounded.

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    Yeah... ask ur doubt

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    why you use Bolzano theorem?

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    Yes... this proof can be partitioned in two levels...in first level, we show that the sequence is bounded and hence ur required answer of boundedness of the Cauchy sequence. If you now wish to prove that the sequence is convergent, then use Bolzano theorem to show the existence of a convergent subseqnce of Un and after that show that Un also converges

  • Anonymous User best-answer

    We know that Cauchy sequence is converget therefore it is bounded.

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    Any doubts please ask.

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    see the attachment.

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