Chashokreddy18@gmail.com posted an Question
September 12, 2020 • 16:36 pm 30 points
  • CSIR NET
  • Mathematical Sciences

Real analysis - difference between finite interval ,finite set, closed set and also difference between infinite interval, infinite set,open set.(p:24)

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    Deepak singh 1 Best Answer

    open interval example - (4,5) . closed interval - example - [4,5]

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    Thank you sir, can both closed set and open set be finite intervals? "All infinite sets are of infinite intervals and all finite sets are of finite intervals".Is this correct?

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    yes , closed set and open set can be finite intervals , eg . (4,5) is open set and of finite intervals..

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    similarly [4,5] is closed set if finite interval..

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    there is language problem in your second statement , there is difference between sets and intervals...a finite interval (0,1) is uncountable set

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    Sir all finite intervals of an open set like (2,4),(3,4), etc.. are uncountable? Please clarify.

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    yes.. you are correct ...

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    Deepak singh 1

    finite set - examples - {set of natural even numbers less than 10 } or { 2,4,6,8} .etc.. infinite set example - set of natural numbers, set of rational numbers etc...

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    Deepak singh 1 best-answer

    A finite interval (bounded interval) is an interval, whose both endpoints are numbers , example - (2,9] , etc.. An infinite interval is an interval, whose at least one endpoint is an infinity examples - (3,infinity) , (- infinity , 3), etc...

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