I dislike the conclusions you have drawn in the face of no references to number theory.
If you don't follow the idea of the geometric sum to infinity and so on, you are better off considering 0.9 recurring as 1-. That is, the non-descript instant before whatever happens at '1' happens. In electronics, this might be the very instant before the switch is flicked, in calculus this might be the value of a limit approaching the left-hand side of a discontinuous point.
You must also be aware that all measured data can only be read to a certain number of significant digits and further calculations on this data cannot have more significant digits than the measured answer. Thus, if you calculate 0.9999, but your most accurate measurement is only to 3 significant figures, the answer is 1.00 (you have to round up).
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branchandroot
(no subject)
Date: 2006-06-20 02:58 pm (UTC)If you don't follow the idea of the geometric sum to infinity and so on, you are better off considering 0.9 recurring as 1-. That is, the non-descript instant before whatever happens at '1' happens. In electronics, this might be the very instant before the switch is flicked, in calculus this might be the value of a limit approaching the left-hand side of a discontinuous point.
You must also be aware that all measured data can only be read to a certain number of significant digits and further calculations on this data cannot have more significant digits than the measured answer. Thus, if you calculate 0.9999, but your most accurate measurement is only to 3 significant figures, the answer is 1.00 (you have to round up).