Principle of Mathematical Induction
The Principle of Mathematical Induction can be informally
stated by saying:
- "We can establish the truth of a proposition if we can show
that it follows from smaller instances of the same proposition,
as long as we can establish the truth of the smallest instance
(or instances) explicitly."
The best way to understand M.I. is to compare it with the Falling Dominoes.
Let's look at a row of dominoes, lined up and ready to be pushed over.
We know from experience that if we push over one domino, the rest of the dominoes will fall over.
Now, if we think of each domino as an instance of a proposition and if we can prove:
The proposition is true in the first instance.
And if a given instance is true, the next one in the sequence will also be true.
Then the proposition will be true in all instances.
This is called a Proof By Mathematical Induction
| 
