Kőnig's lemma

Kőnig's lemma is a result in set theory and combinatorics, particularly in the context of infinite trees. It states that: If every infinite, finitely branching tree has an infinite path, then the tree must have an infinite path. More formally, Kőnig's lemma can be stated as follows: Let \( T \) be a tree such that: 1. Every node in \( T \) has finitely many children (i.e.