(untitled) (Swarnadwar, 2024)
The study of Real Numbers (R) is a fundamental pillar of Mathematical Analysis, serving as the cornerstone for a broad spectrum of Mathematical principles and practical applications. Real Numbers are examined both in theory and in practice, impacting fields like pure Mathematics, physics, engineering, and economics. This paper thoroughly explores Real Numbers, looking at their properties, how they are represented, and their significant role in Mathematical research and various applications. We highlight the importance of Real Numbers in advancing our understanding of Mathematics. This research article provides a comprehensive overview of the Mathematical foundations on Real Numbers and its application in computation. It explores historical developments, theoretical frameworks, Mathematical proofs, comparative analyses, applications, and future directions in the study of Real Numbers. The study aims to synthesize existing knowledge, highlight key contributions, theoretical framework and application in computation.