Sonika posted an Question
September 18, 2020 • 21:06 pm 30 points
  • CSIR NET
  • Mathematical Sciences

What is the meaning of completeness of set of real numbers

what is the meaning of completeness of set of real numbers

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    Deepak singh 1 Best Answer

    This property ensures that there is no "gaps" in the real number line, that is the real number line is continuous. The property is as follows. The Completeness Property of The Real Numbers: Every nonempty subset S of the real numbers that is bounded above has a supremum in R.

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    or we can say any metric space is complete if every cauchy shquence in that space converges in that space too ??? can we diefine completeness proeprty like this ?

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    you are saying definition of complete metric space which is right..

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    I have written definition of completeness property of real no. which is different from complete metric space...

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    Chuppana tanuja

    the set R satisfies 1) field axioms 2) order axioms 3)completeness action and hence R is a complete ordered field

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