Borel Sets

Borel sets are a way mathematicians categorize certain subsets of real numbers based on how they can be constructed. Starting with simple intervals like (a, b), Borel sets include all possible sets you can make by combining countably many intervals through operations like union, intersection, and complement. This creates a large, structured collection of sets that help in analyzing functions, probability, and measure theory. Essentially, Borel sets provide a foundation for understanding which sets are "measurable" and thus can be assigned a meaningful size or probability.