Chapter: Completeness of Real Numbers

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  1. Proposition: The distance of real numbers makes real numbers a metric space.
  2. Definition: Real Cauchy Sequence
  3. Theorem: Completeness Principle for Real Numbers
  4. Theorem: Supremum Property, Infimum Property
  5. Proposition: Convergent Real Sequences Are Cauchy Sequences
  6. Proposition: Not all Cauchy Sequences Converge in the set of Rational Numbers

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