0.999.../Proof by equivalence of Cauchy sequences

< 0.999...

AssumptionsEdit

ProofEdit

In this formalism the task is to show that the sequence of rational numbers

\left(1 - 0, 1 - {9 \over 10}, 1 - {99 \over 100}, \dots\right)
= \left(1, {1 \over 10}, {1 \over 100}, \dots \right)

has the limit 0.