< 0.999...
Assumptions
- Definition from nested intervals
Proof
Applying the nested-intervals definition of the value of an infinite decimal, 0.999... is the unique real number that lies in all of the intervals [0, 1], [0.9, 1], [0.99, 1], and [0.99...9, 1] for every finite string of 9s. Since 1 is an element of each of these intervals, 0.999... = 1.
This article is issued from Wikibooks. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.