What is Function

Duration: 6 min

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Module outline

  1. About Course: About the Course
  2. Paper-2 | Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  3. Paper-2 | Databases / DBMS & SQL: 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
  4. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  5. Paper-2 | Computer Networks & Security: 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 Access Technologies, Network Security
  6. Paper-2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  7. Paper-2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  8. 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
  9. Paper-2 | Computer Organization & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  10. 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
  11. Paper-1 | General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, GK- Current Affairs, History, Geography, Indian Economy, Environment
  12. Paper-1 | Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Data Interpretation, Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Clock, Calendar, Cubes & Dices, Directions (Direction Test), Analogy, Seating Arrangements, Analytical Reasoning (Counting Figures Reasoning)
  13. Paper-1 | Quantitative Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Speed Time and Distance, Average, Age Problems, Percentage, Profit and Loss, Time and Work, Pipe and Cistern, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Mensuration and Geometry, Probability, Statistics, Arithmetic, Algebra
  14. Paper-1 | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Cloze Test (Cloze Passage)
  15. Coal India Previous Year Paper:
  16. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus
  17. Coal India Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a foundational lecture on the mathematical concept of a function. The instructor begins by contextualizing functions as central objects in mathematics. He uses a specific counter-example involving sets X = {1, 2, 3, 4, 5} and Y = {2, 3, 4, 5, 6, 7} to demonstrate why a relation might not be a function. The lecture transitions to a formal definition, explaining that a function must associate every element of a first set with exactly one element of a second set. Key terminology including Domain, Co-Domain, and Range are introduced using set notation and diagrams. The instructor clarifies that the Range is a subset of the Co-Domain.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by stating functions are central to mathematics. He presents a specific example with sets X = {1, 2, 3, 4, 5} and Y = {2, 3, 4, 5, 6, 7}. He displays a diagram where a relation R exists between these sets. He explains this is a valid relation but fails to be a function for two reasons: first, element 3 in set X has no outgoing arrow, meaning it is not participating. Second, element 5 in set X has multiple arrows pointing to 4, 5, and 7 in set Y, violating the "one output" rule. He writes the mathematical hierarchy X * Y >= R >= F on the screen to illustrate that the Cartesian product contains all relations. He circles element 5 to highlight the "one-to-many" violation.

  2. 2:00 – 5:00 02:00-05:00

    The lecture transitions to a formal definition slide. The text states a function associates "every element of a first set exactly one element of the second set." The notation f: A -> B is introduced. A new diagram shows Set X with elements {a, b, c} mapping to Set Y with elements {1, 2, 3}. Here, all elements in X map to 1. The instructor annotates the diagram, labeling Set X as the "Domain" and Set Y as the "Co-Domain". He circles element 1 in Set Y and labels it the "Range". He writes the set-builder notation for Range: {y | y in B and (x, y) in f}. He emphasizes that the Range is a subset of the Co-Domain (Range <= B).

  3. 5:00 – 5:40 05:00-05:40

    The instructor continues to elaborate on the definitions provided in the previous segment. He reinforces the distinction between the Co-Domain (the entire target set Y) and the Range (the specific subset of Y that is actually mapped to). The slide remains visible with the diagram and formulas. The focus is on solidifying the student's understanding of the mapping properties required for a function, specifically the uniqueness of the image for every domain element.

The lesson follows a logical progression from intuition to formalism. It first establishes the necessary conditions for a function by showing violations in a general relation: unmapped elements and one-to-many mappings. This sets the stage for the formal definition where "every element" must map to "exactly one element." The instructor visually distinguishes the Domain (input set) from the Co-Domain (potential output set) and defines the Range as the actual output set. The notation f: A -> B and the set-builder formula for Range are provided for precise mathematical communication. The hierarchy X * Y >= R >= F is used to show that functions are a specific, restricted type of relation.

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