Is 0.9 recurring equal to 1? (for avoidance of doubt, by 0.9 recurring I mean 0.99999…. where the 9s go on forever)
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The issue there is the second line makes a little assumption. That's sort of true only in the limit
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Come on this like the first page of TAOCP
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X=.999999… 10X=9.999999 9X=10X-X=9 X=1
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I'd say no, because 0.999...^inf = 0, whereas 1^inf = 1. But I assume this does not abide by the rules math PhD's made up about what counts as proof, so
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no, because your first equation is false.
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These points are to the left of 1, and they get closer and closer to 1.
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When you define real numbers as the limits or rational numbers a la Dedekind you basically use a math technique to consider these are the same object.
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