Zermelo's theorem is a fundamental result in set theory, established by mathematician Ernst Zermelo in 1904. It states that every set can be well-ordered, meaning that its elements can be arranged in a sequence where every subset has a least element. This theorem is significant because it provides a foundation for understanding the structure of sets and their elements. The proof of Zermelo's theorem relies on the Axiom of Choice, a controversial principle in mathematics. The theorem has important implications in various areas, including ordinal numbers and transfinite induction, influencing how mathematicians approach the study of infinite sets and their properties.