If x and y are any real numbers with x y, then there exists a rational number r ∈ Q such that x…

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If x and y are any real numbers with x lt; y, then there exists a rational number r ∈ Q such that x lt; r lt; y. Using this density argument, show that there exists an irrational number z such that x lt; z lt; y for any real number x and y. (Hint: As √2 is an irrational number, we consider the interval (x/√2, y/√2). Then apply the density argument of Q)

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#MasteringIntegrationTechniquesforOptimalResults
  1. Emily John
  2. Mastering Integration Techniques for Optimal Results
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