L : 05 | CSIR NET DECEMBER 2026 | Real Analysis | Archimedean Property | Supremum & Infimum

🔥 CSIR NET December 2026 Mathematics Complete Course Timestamps: 00:00 – Introduction and Syllabus Overview 00:58 – Definition and Concepts of Intervals (Closed vs. Open) 02:58 – Important Notes on Intervals (Empty and Singleton Sets) 04:07 – Example: Identifying Non-Intervals 06:10 – Types of Intervals and Length of an Interval 07:53 – Detailed Explanation: Open Intervals 08:53 – Detailed Explanation: Closed Intervals 09:27 – Archimedean Property of Real Numbers 10:36 – CSIR NET Dec 2016 Solved Question on Archimedean Property 14:28 – Definition of Greatest Element 15:27 – Bounded Above and Upper Bounds 16:51 – Bounded Below and Lower Bounds 20:20 – Understanding Supremum (Least Upper Bound - LUB) 22:43 – Understanding Infimum (Greatest Lower Bound - GLB) 24:40 – Important Notes on Supremum and Infimum 25:32 – Practice Problems: Finding Supremum, Infimum, and Bounds 32:00 – Definition of a Bounded Set 32:48 – More Solved Examples on Supremum and Infimum 34:28 – Results and Properties of Supremum and Infimum 38:19 – Uniqueness and Existence of Supremum/Infimum 39:42 – Order Completeness in R 40:39 – Conclusion and Preview of Next Lecture (Neighborhood of a Point) Welcome to Tips on Mathematics. In this lecture, we study one of the most important topics of Real Analysis for CSIR NET, GATE, IIT JAM, TIFR, NBHM, SET, TGT & PGT Mathematics. 📚 Lecture 05 Topics ✅ Archimedean Property ✅ Upper Bound & Lower Bound ✅ Supremum (Least Upper Bound) ✅ Infimum (Greatest Lower Bound) ✅ Important Examples ✅ Previous Year Question Concepts ✅ CSIR NET Exam-Oriented Discussion This lecture is highly useful for: CSIR UGC NET Mathematics GATE Mathematics IIT JAM Mathematics NBHM TIFR GS MSc Entrance BSc & MSc Mathematics Students 📲 WhatsApp: 8445721402 📢 Join our channel for complete Mathematics preparation with conceptual explanations and PYQ discussions. 👍 Like | Share | Subscribe | Press the Bell Icon #CSIRNET #CSIRNET2026 #Mathematics #RealAnalysis #ArchimedeanProperty #Supremum #Infimum #CSIRNETMaths #GATEMathematics #IITJAM #NBHM #UGCNET #JRF #TipsOnMathematics #Maths