Non-measurable sets

Non-measurable sets are mathematical collections of points that defy traditional concepts of size or volume. In standard ways of measuring (like length, area, or volume), most sets have a well-defined size. However, some sets are constructed in a way that their "size" cannot be reliably assigned using these measures—these are called non-measurable sets. Their existence reveals limitations in our measurement systems and challenges our understanding of infinity and set theory, illustrating that not all collections of points fit within standard measurement frameworks.