Natural number, Whole number, Integer

Duration: 3 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. CS | 01 | Digital Logic and Circuits and Discrete Mathematical Structures: Digital Systems & Boolean Basics, Number System, Number Representation, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Permutation and Combination / क्रमचय और संचय
  3. CS | 02 | Computer Organization and Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Multiprocessors
  4. CS | 03 | Data Structures and Algorithm: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Complexity Theory, Advanced Algorithms
  5. CS | 04 | Problem Solving through C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. CS | 05 | Object Oriented Techniques: Object Oriented Technology, Java
  7. CS | 06 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Unix OS
  8. CS | 07 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Query Processing & Optimization, File Organization & Indexing
  9. CS | 08 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  10. CS | 09 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  11. CS | 10 | Internet Technology, Web Design and Web Technology: Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, JavaScript-Basics, HTML Basics
  12. CS | 11 | System Analysis And Design: Fundamentals of Systems and Information Systems, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance
  13. CS | 12 | Information Security and Cyber Laws: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security
  14. CS | 13 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  15. GS Paper | 01 | Indian and World Geography / भारत एवं विश्व का भूगोल: Geography / भूगोल
  16. GS Paper | 02 | History / इतिहास: History / इतिहास
  17. GS Paper | 03 | Indian Economy & Social Development / भारतीय अर्थव्यवस्था एवं सामाजिक विकास: Indian Economy / भारतीय अर्थव्यवस्था
  18. GS Paper | 04 | General Science / सामान्य विज्ञान: Biology / जीव विज्ञान, Chemistry / रसायन विज्ञान, Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान
  19. GS Paper | 05 | Elementary Maths / प्रारंभिक गणित: Number System / संख्या पद्धति, Divisibility Rules / विभाज्यता के नियम, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Percentage / प्रतिशत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Ratio and Proportion / अनुपात और समानुपात, Average / औसत, Time and Work / समय और कार्य, Time, Speed and Distance / समय, चाल और दूरी, Algebra / बीजगणित, Solid Mensuration / घन क्षेत्रमिति, Data Interpretation / आँकड़ा निर्वचन, Arithmetic / अंकगणित, Statistics / सांख्यिकी, Probability / प्रायिकता, Sequences, Series and Combinatorics / अनुक्रम, श्रेणी और संयोजन, Mixture and Alligation / मिश्रण और एलिगेशन, Calculus / कलन, Trigonometry / त्रिकोणमिति, Vectors / सदिश, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Euclidean Geometry and Mensuration / यूक्लिडीय ज्यामिति और क्षेत्रमिति, Statistics and Probability / सांख्यिकी और प्रायिकता, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ, Plane Mensuration / समतल क्षेत्रमिति, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित
  20. GS Paper | 06 | Indian Polity and Governance / भारतीय राजव्यवस्था एवं शासन: Polity / राजव्यवस्था
  21. GS Paper | 07 | Current Events / समसामयिक घटनाएँ: Current Affairs / समसामयिकी
  22. UPLT Live Classes Notes: UPLT Live Classes
  23. UPLT Full Mock Tests Tier 1:
  24. UPLT Full Mock Tests Tier 2:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a foundational overview of number systems, focusing on Natural numbers, Whole numbers, Integers, and Irrational numbers. The instructor utilizes textual definitions, set notation, hierarchical diagrams, and number lines to explain the properties and relationships of these mathematical sets. The lecture aims to clarify the distinctions between different types of numbers and how they fit into the broader category of Real numbers and their properties.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by defining Natural numbers (N) as numbers occurring in nature, represented by the set N = {1, 2, 3, 4.... infinity}. A number line from 0 to 10 is displayed with arrows indicating that Natural Numbers start from 1, while Whole Numbers start from 0. A hierarchical tree diagram illustrates the relationship between Complex, Real, Rational, and Irrational numbers, narrowing down to Natural numbers at the bottom. The instructor circles 1, 2, and 3 on the number line to visually reinforce the concept of natural numbers. He emphasizes that these are the numbers we use for counting. The slide text explicitly states "A natural number is a number that occurs commonly and obviously in nature."

  2. 2:00 – 2:59 02:00-02:59

    The lesson transitions to Whole numbers (W) and Integers (Z). Whole numbers are defined as an expanded set of natural numbers including zero, written as W = {0} U N. The instructor draws a number line extending to negative infinity to represent Integers, defined as numbers without fractional components. He writes the set notation W = {0} U N on the whiteboard area. Finally, the concept of Irrational numbers is introduced with the definition that they cannot be expressed as a ratio of integers and have non-terminating, non-repeating decimal expansions, citing root 2 as an example. The hierarchy chart is revisited to show Irrational numbers as a subset of Real numbers, distinct from Rational numbers.

The video systematically builds the number system hierarchy. It starts with the most basic counting numbers (Natural), expands to include zero (Whole), adds negative counterparts (Integers), and finally introduces non-repeating decimals (Irrational). The visual aids, particularly the number lines and the tree diagram, are crucial for understanding the subset relationships between these sets. The instructor uses both verbal explanations and written notations to clarify the definitions. The progression moves from simple counting to more abstract concepts like irrationality, providing a comprehensive overview of real number classification. The clear distinction between terminating/repeating decimals (Rational) and non-terminating/non-repeating decimals (Irrational) is a key takeaway. This structured approach helps students grasp the logical flow of number theory.

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