👉 Russell's Math, or simply Russell's system, is a formal axiomatic approach to set theory developed by Bertrand Russell in the early 20th century. It aims to provide a rigorous foundation for mathematics by defining sets and their properties through a set of precise logical axioms. The core of this system is based on a hierarchy of types to avoid paradoxes, such as Russell's paradox, which arises from considering a set of all sets that do not contain themselves. In Russell's framework, sets are constructed in stages, starting from the simplest (zero sets) and building up to more complex ones, ensuring that no set can contain itself or any set that leads to a contradiction. This method not only clarifies and standardizes mathematical concepts but also lays the groundwork for modern set theory, influencing fields like logic, philosophy, and computer science.
