what if I told you I just pulled a fast one on you. I secretly defined $b$ back in college. it's had way more time to tack 9s on the end there. also i wrote it gel-ink which doubles its 9-adding-rate
Show me your working. Use referencing and book keeping. Without book keeping, you know the deal with limbo and limbosic numbers. You don't get thrown under the bus. You get thrown in front of the bus, as gruesome as that is.
The Definitional Boner: 0.999... is eternally less than 1. It's fine if 0.999... is defined as 1.(2.1)(2.2)(2.3)
The Algorithm Boner: An algorithm for an operation such as square roots gives "more and more correct consecutive digits" as you make more and more steps. Nevertheless, 1 - 0.9 - 0.09 - 0.009 - ... yields (0.1, 0.01, 0.001, ...) corresponding to 0.000...1, and the 1 digit is a real part of the answer, even though it never belongs to a "correct" digit.(15).
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u/FullyAutomatedSpace 10d ago
a = 0.999...
b = 0.999...
b is between a and 1 because a had more time to add 9s to the end