diagonalization

Diagonalization is a mathematical technique that constructs a new object by systematically differing from each item in a list along a "diagonal" path.

The method is most famous in Cantor's proof that real numbers outnumber integers: you build a number that differs from the first listed number in its first digit, from the second in its second digit, and so on—guaranteeing a number not on any supposedly complete list.

The technique extends to logic and computer science, proving that some problems are undecidable.

In linear algebra, diagonalization transforms a matrix into diagonal form, simplifying calculations.