Natural number, Whole number, Integer

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/MPPSC-ASSISTANT-PROFESSOR-COMPUTER-SCIENCE-PAPER-2/unit-i-discrete-mathematical-structure/set-theory/sets-representation-of-sets-and-hierarchy-of-numbers/asset-natural-number-whole-number-integer after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 1 | General Studies: State Wise GK / राज्यवार सामान्य ज्ञान (GK)
  3. Paper 1 | Information and Communication Technology: Role of Internet and Web Services, Security in Mobile and Wireless Computing
  4. Paper 1 | Current Affairs: GK- Current Affairs / GK- समसामयिकी
  5. Paper 2 | Discrete Mathematical Structure: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  6. Paper 2 | Digital Computer Organization And Architecture: Number System, Number Representation, Sequential Circuits, Combinational Circuit, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. Paper 2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  8. Paper 2 | Programming Languages & Object-Oriented Programming Concepts: Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  9. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  10. Paper 2 | Data Structure And Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Advanced Algorithms
  11. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS
  12. Paper 2 | Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  13. Paper 2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  14. Paper 2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Enhanced Data Models
  15. Paper 2 | Computer Network And Information Security: Introduction to CN, Data Communication, Application Layer, Hardware basics, Cyber Threats and Malware Attacks, Network Security, 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
  16. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  17. Paper 2 | Current Trends & Technologies: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms, Data Warehousing & Mining, Electronic Data Interchange and E-Commerce
  18. Paper 2 | Full Length Mock Tests:
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.

Loading lesson…