Theorem on Supremum | Supremum | Important Theorem | Real Analysis | For B.Sc. , Ba, M.Sc.
Welcome to our deep dive into one of the fundamental concepts in Real Analysis: the Supremum Theorem. Whether you're a student pursuing a B.Sc., BA, or M.Sc., this video is designed to give you a clear and comprehensive understanding of the supremum and its significance in mathematics.
🔍 What You Will Learn:
- Definition of Supremum: Understand what the supremum (or least upper bound) of a set is and how it differs from the maximum.
- Supremum Theorem: Explore the formal statement of the supremum theorem and its proof.
- Applications and Examples: See practical examples that illustrate how to find the supremum of different sets and understand its applications in real-world problems.
- Important Theorems Related to Supremum: Get insights into other key theorems in real analysis that involve the concept of supremum, such as the Completeness Property of the Real Numbers.
📘 Who Should Watch:
- B.Sc. and BA Students: Simplified explanations and examples to help you grasp the basics.
- M.Sc. Students: In-depth discussion and proofs for a thorough understanding.
- Anyone Interested in Mathematics: Clear and engaging content that makes advanced concepts accessible.
🔗 Timestamps:
0:00 - Introduction
0:43 - Supremum Property of Relation
2:38 - Infimum Property of Relation
15:52 Theorem - 2
18:25 - Proof of I Part
25:02 - Proof of II Part
42:27 - End
Join us on this educational journey to master the concept of supremum and strengthen your foundation in real analysis. Don't forget to like, comment, and subscribe for more educational content!
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