Entroper on 01 June 2007
The .3333... argument is the easiest to understand. The real "discrete math" proof does say that between any two real numbers are an uncountabily infinite number of real numbers. So you would have to find a number that is between .9999... and 1. jlauro's argument (.9999... + 1)/2 doesn't work, because it assumes that .9999... and 1 are not the same number. You can't assume the thing you are trying to prove! If they are equal, then the average of the two numbers is also equal, and therefore not between them. Happy, .9999... is a rational number. It can be expressed as the ratio between 1 and 1. See the 1/3 argument above.
