Contrary to what most [[mathematician]]s believe, [[Georg Cantor]]'s first proof that the set of all [[real number]]s is [[uncountable set|uncountable]] was not his famous [[Cantor's diagonal argument|diagonal argument]], and did not mention decimal expansions or any other [[numeral system]]. The original theorem and proof below were found by Cantor in December 1873, and published in 1874 in ''[[Crelle's Journal]]'', more formally known as ''Journal für die Reine und Angewandte Mathematik'' (German for ''Journal for Pure and Applied Mathematics''). Cantor discovered the diagonal argument in 1877.
