The Erdős–Szekeres Theorem is a fundamental result in combinatorial mathematics that deals with sequences of numbers. It states that for any sequence of n distinct real numbers, if n is greater than or equal to k \times m , then the sequence contains either an increasing subsequence of length k or a decreasing subsequence of length m . This theorem highlights the inherent order within sequences and has applications in various fields, including computer science and graph theory. It was independently proven by mathematicians Paul Erdős and George Szekeres in 1935, establishing a key concept in the study of order and structure in mathematics.