The Principle Of Mathematical Induction
Chapter Name : Principle Of Mathematical Induction |
Sub Topic Code : 104_11_04_03_02 |
Topic Name : The Principle Of Mathematical Induction |
|
Sub Topic Name : Some Examples |
|
Introduction
• In Mathematics, there are certain statements which are formulated in terms of n where n is a positive number. • To prove such statements a well suited principle is formed which is known as Principle of Mathematical Induction. • In this topic we will solve different problems on principle of mathematical Induction.
Pre-Requisites:
Basic knowledge of Set Theory. Basic knowledge of Sequences and Series. Knowledge on Principle of Mathematical Induction.
Activity:
Observation is suppose there are 6 pieces of rectangular pieces then minimum breaks required is 5.
Real Life Question:
How many breaks are required to break your favourite Cadbury chocolate?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| N | Set of all Natural numbers(set theory) |
| Hypothesis | A supposition based on reasoning. It is taken for granted for further proving statement. |
| Induction | A two part way of proving a theorem. First the theorem is proved for smallest value of integer. If the theorem is true for any value of integer then it is proven that the theorem is true for the next greater value. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Cadbury chocolate | Task is to break your chocolate with minimum number of breaks into individual rectangular pieces. |
Real life uses :
Induction is also called as Inductive Reasoning. We use reasoning everyday in our daily life. For example that every time you eat spicy pizza your stomach gets upset and you should stop eating them. What we have observed is we are moving from a particular observation to a general conclusion. So indirectly we have applied here induction.
Places to visit :
Play bowling game and observe principle of mathematical induction.
Practical examples around us
| Examples | Explainations |
|---|---|
| Principle of Mathematical Induction | Principle of Mathematical Induction is very powerful tool in solving functional analysis proofs. Analysis is very useful in Environmental sciences, Life sciences etc. |
What you learn in Theory:
Principle of Mathematical Induction is a process of solving larger complex problems by organizing the problem into smaller portions.
What you learn in Practice:
Principle of Mathematical Induction can be used in various puzzle games.