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The name "Mathematical Induction" was first used by the English Mathematician Augustus De - Morgan (1809 - 1871) in his article on "Induction Mathematics". However the credit of origin of principle of Induction goes to Italian Mathematician Francesco Mau Rolycus (1494 - 1575). The Indian Mathematician Bhaskara (1153) had also used traces of "Mathematical Induction" in his writings.

Augustus De - Morgan (1809 - 1871)


Giuseppe Peano (27 August 1858 - 20 April 1932) was an Italian mathematician, made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction.

Observe the row of dominoes, lined up and are ready to be pushed over.
The following visual clearly gives us the experience, that if we push over one domino, the rest of the dominoes will fall over.
How does this happen?
  1. From the visual, we observe that, if we push over one domino, it falls over.
  2. We also observe that if a domino is falling and has been placed correctly, it is knocking over its neighbor. 
Intuitively, it is evident that the fall should cascade all the way up to the last domino.  That is, if the next to the last domino falls, the last domino also falls.

The behaviour of the dominoes can be formulated as a formal proof as follows:
  • If we knock over the first domino,
  • and a falling domino knocks over its neighbor.
  • then all the dominoes will fall over.
Thus if we can establish,  
  1. The proposition is true for the first instance.
  2. And if a given instance is true, the next one in the sequence will also be true.
  3. Then the proposition will be true in all instances.
This method of proof is called "Induction principle".

In Mathematics, deductive reasoning is more commonly used. Deduction is an application of a general case to a particular case. For example, using identity we can deduce. This is a case of application is in natural numbers. Similarly the same identity can be used in complex numbers.

Eg:  (complex numbers is Ch. 5)

In contrast to deduction, inductive reasoning depends on generalising a statement after it is known to be true in some particular cases. But this has to be handled very carefully as a statement need not be universally true just because it is true for some particular cases.

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