Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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A logical argument devised by [[Georg Cantor]] to demonstrate that the [[real numbers]] are not [[countably infinite]]. It proceeds as follows: #Suppose the [[real numbers]] are countably infinite. #We may now enumerate them as a sequence, {r_{1},r_{2},r_{3},...} #We shall now construct a real number, x, by considering the nth digit of the decimal expansion of r_{n}. Our real number x will be between 0 and 1. ::If the nth digit of r_{n}is 0, let the nth in digit the decimal expansion of x be 1 ::Otherwise, let the nth in digit the decimal expansion of x be 0 x is clearly a real number, but it differs in the nth decimal place from r_{n}, so x is not in our enumeration of the real numbers. This contradicts our supposition that the reals are countably infinite, and therefore our supposition is false. The diagonal slash argument is an example of [[reductio ad absurdum]]. ''Is the diagonal slash argument the usual term for this? I've seen it many times, in various sources and on the internet, and I don't think I've ever seen the word slash applied to the title. Usually it's just something like the diagonalization argument.''