Anku posted an Question
February 21, 2021 • 12:46 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Why is this uncountable..can't we use fact finite product of countable sets is countable in this question.

why is this uncountable..can't we use fact finite product of countable sets is countable in this question.

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    Deepak singh 1 best-answer

    take (π,1/π) belongs to R^2 and π×1/π = 1 which belongs to Z , thus it implies this set contains irrational no. also and irrational are uncountable , so given set is uncountable .

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    sir then it should also be uncountable as √8,√2 € R and their product is √(16)=4 € Q and since set of irrational numbers so uncountable ....but ans given is countable

    eduncle-logo-app

    sir pls tell my mistake..

    eduncle-logo-app

    wait..

    eduncle-logo-app

    it should be uncountable also , because this set is containing irrational also..

    eduncle-logo-app

    if you have any explanation proving countable then you please share..

    eduncle-logo-app

    ok sir .

    eduncle-logo-app

    feel free to ask again..

    eduncle-logo-app

    sir this explanation is there in book

    eduncle-logo-app

    but i did not got for option c and d

    eduncle-logo-app

    Dear , in option d , there is a,b not a.b

    eduncle-logo-app

    oohh..i got it sir..

    eduncle-logo-app

    since there is a,b . So it will be countable ..

  • Alka gupta best-answer

    here we can not statblis one one correspondence to given set....so thats y it is uncountable set

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