How does the infinite repeating decimal 0.999… differ from any finite truncation such as 0.999?
Answer & explanation
The limit is 1; finite truncations are lower.
A truncation with n nines differs from 1 by 10⁻ⁿ. Those gaps have limit zero. There is no positive fixed gap left in the infinite decimal.
How Not to Be Wrong
Chapter 2 · Straight Locally, Curved Globally
AI reviewed · sources pending · version 8
Generally accurate according to an AI review. Sources and this book association have not been verified.