impossible statements

Michael Hill · #23 13-08-2005, 11:30

Why 9.999... =/= 1

Code:

       x = 0.9999...
     10x = 9.9999...
 10x - x = 9.9999... - 0.9999...
      9x = 9
       x = 1

This may seem correct, but I believe it is not. In the second step when you multiply it by 10, you will get soemthing like 9.9999.....0. There must be a 0 on the end. This is because there are no longer infinity 9s at the end. There are infinity minus 1. I'll explain another way that I believe may be a little more correct (because I'm not 100% sure on my previous statement). 1 does not equal .9999.... because 1 - .0....01 = .9999... This proves for as many 9s you add at the end, it will never quite equal 1.

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