11b: Properties of Supremum and Infimum of a set || Show that Sup(a+S)=a+SupS || Real Analysis

Principles of Mathematical Analysis || Real Analysis || Walter Rudin Lecture # 11b In this lecture I will discuss a property related to supremum of a set, that can be stated as: If S is a non-empty bounded above subset of R, then show that Sup(a+S)=a+SupS, where a is any real number. ------------------------------------------------------------------------------------------------------------------------------------------------------- This lecture series on Real Analysis, based on "Principles of Mathematical Analysis" by Walter Rudin, is designed to help students understand key concepts in this foundational subject. While particularly useful for students taking Real Analysis courses such as MATH2400 at the University of Queensland and MAST20026 at the University of Melbourne, the material is broadly applicable to anyone studying graduate-level mathematics. Whether you are preparing for exams or looking to deepen your understanding, these lectures will provide valuable insights and comprehensive explanations. ------------------------------------------------------------------------------------------------------------------------------------------------------- 📚 Important Course Playlists ▶️ Link to Real Analysis/ Principle of Mathematical Analysis by Walter Rudin    • Mastering Real Analysis: Walter Rudin's Pr...   ▶️ Link to Introduction to Operations Research by Frederick S. Hillier, Gerald J. Lieberman (late)    • OPERATIONS RESEARCH   ▶️ Link to Complex Analysis    • COMPLEX ANALYSIS|| HIGHER MATHMATICS|| PRO...   ▶️ Link to 13 Core areas of Number Theory    • Comprehensive Number Theory Course: 13 Cor...   --------------------------------------------------------------------------------------------------------------------------------------------- #CompletenessProperty #WalterRudin #MathematicsLectures #HigherMathematics #MathForBSStudents #CompleteField #RealNumbers #matheducation #RealAnalysis, #SupremumAndInfimum, #Mathematics, #MathLectures, #SupremumProperties, #InfimumProperties, #UniqueSupremum #RealAnalysis #Mathematics #UniversityOfQueensland #UniversityOfMelbourne #Math2400 #mast20026 #MathematicsLecture #AdvancedMath #SetTheory #AdvancedMathematics #PrinciplesOfMathematicalAnalysis #highermathematics #professorazmatali #maths4u @azmatali009 @azmatali006