The diagonal argument, introduced by Cantor in 1891, proves some infinities are strictly larger than others by constructing an object that evades any proposed complete list or mapping. This same self-referential trick underlies Cantor's theorem, Turing's halting problem, and Gödel's incompleteness theorem—one idea unifying set theory, computability, and logic.

In this article, we will model the time complexity of divide and conquer using mathematical methods, analyze its asymptotic properties, and provide three methods of calculation.