Dedekind Cut : “Prove 0.9999… = 1”

Key Notes:

  1. Rational Numbers Q eg. 1/2, … Complete but non Continuous.
  2. Irrational numbers eg. \sqrt {2}
  3. Real number is Complete and Continuous
  4. Dedekind Cut

The Proof of “0.999… = 1” by using Set Theory :

A \subset B
and
B \subset C
\implies A = B

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