The "NET-JRF (Mathematical Science) Book - Exploring Set Theory and Real Number Foundations" is a comprehensive and meticulously crafted resource designed to assist candidates preparing for the National Eligibility Test (NET) in Mathematical Sciences. This book delves into the foundational aspects of mathematics, specifically focusing on elementary set theory and the real number system. It is an indispensable tool for aspiring mathematicians, educators, and researchers who seek a deep understanding of these fundamental concepts.