For any positive real number x, prove that there exist an irrational number y such that 0

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For any positive real number x, prove that there exist an irrational number y such that 0

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Emery 4 days 2021-10-11T15:16:47+00:00 1 Answer 0 views 0

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    2021-10-11T15:18:33+00:00

    Correct Question:-

    For any positive real number x, prove that there exist an irrational number y such that 0 < y < x

    AnswEr:-

    ★ If x is irrational,

    Then \sf y = \dfrac{x}{2} is also an irrational number such that 0 < y < x.

    ★ If x is rational,

    Then \sf y = \dfrac{x}{ \sqrt{2}} is an irrational such that

    \sf y = \dfrac{x}{ \sqrt{2}}\qquad\bigg\lgroup\bf as\; \sqrt{2} > 1\bigg\rgroup

    Hence, for any positive real number x, there exists an irrational number y such that 0 < y < x.

    \rule{200}3

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