Cantor's diagonal argument
Cantor's diagonal argument is a mathematical method to prove that two infinite sets have the same cardinality. Cantor  published articles on it in 1877, 1891 and 1899. His first proof of the diagonal argument was published in 1890 in the journal of the German Mathematical Society (Deutsche Mathematiker-Vereinigung).  According to Cantor, two sets have the same cardinality, if it is possible to associate an element from the second set to each element of the first set, and to associate an element of the first set to each element of the second set. This statement works well for sets with a finite number of elements. It is less intuitive for sets with an infinite number of elements.