It is a commonly held misconception that 0.99.. = 1. However there is a number denoted b(1) [Bassett one] such that 0.99.. < b(1) < 1. The set of all Bassett numbers, B, is construsted by first placing the real line on a sheet of rubber. The sheet is then stretched, until eventually holes appear between numbers. These numbers are then filled by the Bassett numbers.
An interesting property of the Bassett numbers is that they are "chunky". Points on the real line are represented by lines of finite height but zero width. Now, all numbers have the same area, and since the holes that B fills have a width greater than zero, the Bassett numbers must be a lot shorter than the real numbers. Hence they are pretty stout fellows and are chunky.
The Bassett numbers were originally constructed by Laurence C.P. Bassett.