# 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
$B \subset C$
$\implies A = B$