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0.999… revisited
so that number to me should be 0.999… but it is not where am I missing the point? Physicist: In the language of mathematics there are “dialects” (sets of axioms), and in the most standard, commonly-used dialect you can prove that 0.999… = 1. The system that’s generally taught now is used because it’s useful (in a lot of profound ways), and in it we can prove that 0.99999… = 1. In the system of real numbers every number can be added, subtracted, multiplied, and divided without “leaving” the real numbers. Point is: it’s tempting to say that 0.999… is the “first number below 1”, but that’s not a thing.
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