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this post was submitted on 17 Jul 2023
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The difference between 0.999... and 1 is 0.
It is possible to define a number system in which there are numbers infinitesimally less than 1, i.e. they are greater than every real number less than 1 (but are not equal to 1). But this has nothing to do with the standard definition of the expression "0.999...," which is defined as the limit of the sequence (0, 0.9, 0.99, 0.999, ...) and hence exactly equal to 1.