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Math and Science / Re: .9 repeating equals 1?
« on: January 10, 2014, 02:45:02 pm »
The following is an argument that makes sense to me: two real numbers are different if and only if their difference (the result of subtracting them) is not 0. If we look at the result of subtracting .9repeating from 1, it is certainly nonnegative, but it is also less than .1, .01, .001, and so on. So whatever this number is, if it is positive, we can find a (negative) power of 10 that is smaller than it and that it must be smaller than. Since two numbers x and y cannot have both x>y and x<y, we have arrived at a contradiction. Therefore, this number cannot be positive, and must be 0.