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Peter Linz Edition 5 Exercise 11.1 Question 19 (Page No. 284)

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Show that the set of all irrational numbers is not countable.
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We know  real no = rational + irrational .

  • Rational number is countable
  • Real number is uncountable.

Then irrational number must be uncountable . 

If we take irrational number is countable then real number become countable . So it cant be possible.

 

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