Real Analysis | Lecture 2 | Countable & Uncountable Sets | Cardinality, Power Set & Cantor’s Theorem

📌 Visit description resources for additional notes and practice problems. Real Analysis Lecture 2 | Countable & Uncountable Sets | Cardinality, Power Set & Cantor’s Theorem | BSc Sem 2 (NEP 2020) In this lecture, we explore deeper concepts of Set Theory in Real Analysis for BSc Mathematics Semester 2 (as per NEP 2020). This session covers the structure, size, and classification of sets, along with important theorems that form the foundation of higher mathematics. 🔹 Topics Covered: • Similar (Equivalent) Sets • Equal Sets • Countable (Enumerable) Sets • Uncountable Sets • Cardinality of Sets • Aleph-Null & Continuum • Power Set • Injective, Surjective & Bijective Functions • Relationship between a Set and its Power Set • Cantor’s Theorem (Proof Overview) This lecture is essential for building a strong foundation in Real Analysis and understanding infinite sets rigorously. ⏱️ Timestamps 00:00 – Introduction 00:48 – Similar (Equivalent) Sets 05:16 – Equal Sets 08:30 – Countable (Enumerable) Sets 12:18 – Uncountable Sets 15:18 – Cardinality of Sets 18:07 – Power Set 26:45 – One-to-One & Onto Functions 36:15 – Cardinality vs Power Set Theorem 46:31 – Cantor’s Theorem (Proof) 👍 Like | 🔁 Share | 🔔 Subscribe 🔑 Keywords Real Analysis Lecture 2 Countable and Uncountable Sets Cardinality of Sets Power Set theorem Cantor’s Theorem proof Aleph null Continuum hypothesis basics Equivalent sets Bijective function BSc Mathematics Semester 2 NEP 2020 Mathematics Set Theory lecture Undergraduate Real Analysis 📢 Hashtags #RealAnalysis #SetTheory #CantorTheorem #Cardinality #PowerSet #BScMathematics #NEP2020 #MathLecture #InfiniteSets #UndergraduateMath