#3 Axioms of Real Numbers | Real Analysis | TGT PGT 2026 | New Updated Syllabus | by yash sir

#3 Axioms of Real Numbers | Real Analysis | TGT PGT 2026 | New Updated Syllabus | Feeling Wali Class by yash vardhan tengauriya sir Welcome to Tengauriya Concept – Maths by Yash Vardhan Tengauriya ❤️ ABOUT THE EDUCATOR: Yash Vardhan Tengauriya Assistant Professor at Shri Gaurishankar Degree College M.Sc., B.Ed. (Mathematics) Currently Pursuing Ph.D. in Mathematics Motivational Speaker Higher Mathematics Educator ━━━━━━━━━━━━━━━━━━ 📚 IMPORTANT LINKS: 🔹 LCD Complete Course 2026 Playlist    • UP TGT/PGT 2026 | REAL ANALYSIS | LCD Comp...   🔹 Relation & Function Complete Course Playlist    • UP TGT/PGT 2026 | Algebra - Set Theory, Ma...   🔹 Real Analysis Complete Course Playlist    • UP TGT/PGT 2026 |  Real Analysis – Sequenc...   🔹 Theory of Equation & Group Theory    • UP TGT/PGT 2026 | Algebra – Theory of Equa...   🔹 WhatsApp Boys Group https://chat.whatsapp.com/CpiAkpuwFpV... 🔹 WhatsApp Girls Group https://chat.whatsapp.com/HIg4qDoK7KS... 🔹 Telegram Channel https://t.me/TengauriyaConcept 🔹 Instagram   / yashvardhantengauriya   🔹 Facebook Page   / tengauriyaconcept   ━━━━━━━━━━━━━━━━━━ 📖 ABOUT THIS LECTURE: Welcome to the NEW REAL ANALYSIS COMPLETE COURSE 2026. This is Lecture-3 of Real Analysis, where we begin from the most fundamental foundation of the subject — AXIOMS OF REAL NUMBERS. Real Analysis sirf formulas ya definitions yaad karne ka subject nahi hai. Isme concepts ki depth, mathematical logic aur reasoning sabse important hoti hai. Is lecture mein Tengauriya Sir Real Numbers ke fundamental axioms ko basic se advanced level tak explain karenge, taaki aage ke Real Analysis concepts ko strong mathematical foundation ke saath samjha ja sake. 🎯 This series is designed according to the NEW UPDATED SYLLABUS approach for UP TGT & PGT Mathematics 2026 preparation. Basic se Advanced tak — Real Analysis ko sirf padhenge nahi, FEEL karenge. ❤️ ━━━━━━━━━━━━━━━━━━ 🔥 TOPICS COVERED IN LECTURE-1: • Real Numbers — Introduction • Axiomatic Approach to Real Numbers • Axioms of Real Numbers • Field Axioms • Properties of Real Numbers • Algebraic Structure of Real Numbers • Order Properties • Mathematical Logic Behind Real Numbers • Important Concepts for Real Analysis • Exam-Oriented Concept Building • Common Conceptual Mistakes • Foundation for Further Real Analysis Topics ━━━━━━━━━━━━━━━━━━ 🎯 TARGET EXAMS: UP TGT Maths 2026 UP PGT Maths 2026 NVS Mathematics KVS Mathematics LT Grade Mathematics EMRS Mathematics Other Teaching & Competitive Mathematics Exams ━━━━━━━━━━━━━━━━━━ 💡 WHY THIS REAL ANALYSIS COURSE? Real Analysis ko ratna nahi hai. Concept ko samajhna hai. Logic ko feel karna hai. Questions ko approach karna hai. Aur Mathematics ko deeply understand karna hai. This complete course focuses on: ✅ Conceptual Clarity ✅ Mathematical Logic ✅ Strong Fundamentals ✅ Exam-Oriented Preparation ✅ Important Questions ✅ Problem-Solving Approach ✅ Basic to Advanced Learning No unnecessary memorization. No fear of Higher Mathematics. ONLY — CONCEPT + LOGIC + QUESTIONS + FEELING WALI TEACHING. ❤️ ━━━━━━━━━━━━━━━━━━ 🚀 NEW SYLLABUS • NEW SERIES • NEW APPROACH Aaj se Real Analysis ki ek powerful journey shuru ho rahi hai. Pehla step — AXIOMS OF REAL NUMBERS. Aage Limits, Continuity, Differentiability, Sequences, Series aur Real Analysis ke important concepts ko step-by-step cover karenge. Agar aap UP TGT/PGT Mathematics 2026 ki serious preparation kar rahe ho, to is series ko miss mat karna. SUBSCRIBE to Tengauriya Concept and prepare Mathematics with concepts, not shortcuts. CONCEPT MAKES A PERFECT. ❤️ ━━━━━━━━━━━━━━━━━━ #RealAnalysis #AxiomsOfRealNumbers #RealNumbers #RealAnalysis2026 #TGTMaths #PGTMaths #UPTGT2026 #UPPGT2026 #UPTGTMaths #UPPGTMaths #TGT2026 #PGT2026 #Maths2026 #TengauriyaConcept #TengauriyaSir #YashVardhanTengauriya #FeelingWaliClass #HigherMathematics #MathematicalAnalysis #NVS2026 #KVS2026 #LTGrade #EMRS2026 #TeachingExamPreparation #CompetitiveMaths #FreeMathsCourse #RealAnalysisForTGT #RealAnalysisForPGT #NewSyllabus2026 ━━━━━━━━━━━━━━━━━━ 5+ Years Teaching Experience Educator at Tengauriya Concept Known for Feeling Wali Classes 🔥 REAL ANALYSIS SERIES STARTED! Aaj se Real Analysis ko zero se advanced level tak samjhenge — bina unnecessary ratta, bina confusion. Concept clear hoga, tabhi Mathematics strong hogi. ❤️ #TengauriyaConcept #FeelingWaliClass #RealAnalysis #UPTGT2026 #UPPGT2026