One-To-One (Injective Function)

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/ISRO/discrete-mathematics/functions/one-to-one-injective-function-definition-count-and-properties/asset-one-to-one-injective-function after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. General Aptitude & Reasoning: Number System, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Speed Time and Distance, Mixture and Alligation, Data Interpretation, Algebra, Probability, Permutation and Combination, Venn Diagram, HCF LCM, Divisibility Rules, Age Problems, Pipe and Cistern, Partnership, Linear Algebra, Sequence and Series (Series), Statistics, Powers and Exponents (Surds and Indices), Arithmetic, Mensuration and Geometry, Calculus, Trigonometry, Vectors, Speed Mathematics and Basic Mathematics, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analogy, Series (Number and Letter Series) (Numerical Relations and Reasoning), Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Calendar, Seating Arrangements, Coding Decoding, Blood Relations, Directions (Direction Test), Clock, Analytical Reasoning (Counting Figures Reasoning), Ranking, Order and Sequence, Logical Sequence Of Words, Inequality, Data Sufficiency, Cubes & Dices
  3. Computer Networks & Cybersecurity: 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, Network Security
  4. Programming, Data Structures & Algorithms: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, 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, Advanced Algorithms
  5. AI, Machine Learning, Big Data & Cloud: Emerging Tech Trends, Artificial Intelligence, Big Data Systems, Approaches to AI, Search Algorithms, Knowledge Representation, Cloud Computing
  6. Digital Logic & Computer Organization: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, 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. TOC & Compiler: 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, 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
  8. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  9. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Distributed Systems
  10. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Object Oriented Technology, HTML Basics, JavaScript-Basics, Java, XML
  11. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Data Warehousing & Mining, Enhanced Data Models, NoSQL
  12. Other Recurring CS Topics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, Multimedia
  13. Live Classes: ISRO Live classes
  14. Full Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a detailed explanation of One-to-One (Injective) functions in set theory. The instructor begins by presenting the formal definition on a slide, stating that a function F: A -> B is one-to-one if every element of the domain A has a distinct image in the codomain B. He emphasizes the condition for finite sets, noting that a one-to-one mapping is possible only if the cardinality of set A is less than or equal to the cardinality of set B. The lecture utilizes visual diagrams to illustrate valid mappings and concludes with a handwritten example to reinforce the concept of distinct images.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the topic "One-to-One (Injective Function)" and reads the definition from the slide. He uses a red pen to underline the phrase "one-to-one function" and the critical condition "every element of A has distinct image in B". He then discusses the constraint for finite sets, underlining the inequality "|A| <= |B|". He points to two diagrams on the slide: the left diagram shows a function from X={1, 2, 3} to Y={A, B, C, D} where 1 maps to D, 2 maps to B, and 3 maps to A, leaving C unmapped. The right diagram shows a function from X={1, 2, 3, 4} to Y={A, B, C, D} where every element maps distinctly. This visual comparison helps students understand that unused elements in the codomain are allowed in one-to-one functions.

  2. 2:00 – 3:16 02:00-03:16

    To further clarify, the instructor draws a new example on the right side of the screen. He writes "X" and "Y" as headers for two sets. Under X, he lists elements {1, 2, 3}, and under Y, he lists {a, b, c}. He draws arrows to show a mapping: 1 -> a, 2 -> b, and 3 -> c. He circles the entire set X and the entire set Y with red ink to visually separate the domain and codomain. This specific example demonstrates a scenario where the number of elements in the domain equals the number of elements in the codomain, satisfying the one-to-one condition perfectly. The instructor's hand movements guide the viewer's attention to the specific mappings being created.

The lesson progresses logically from theoretical definitions to practical application. By first establishing the formal rules and cardinality constraints, the instructor sets a strong foundation for understanding injective functions. The transition to visual diagrams and finally a hand-drawn example allows students to see the concept in action. The consistent use of red underlining and drawing highlights key mathematical relationships, ensuring that the distinction between domain and codomain elements is clear throughout the lecture. This multi-modal approach reinforces the learning objective effectively.

Loading lesson…