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Plus one Mathematics
Chapter 4
Principle of mathematical induction
Malayalam class.
principle of mathematical induction class 11 malayalam
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Summary
One key basis for mathematical thinking is deductive reasoning. In contrast to
deduction, inductive reasoning depends on working with different cases and
developing a conjecture by observing incidences till we have observed each
and every case. Thus, in simple language we can say the word ‘induction’
means the generalisation from particular cases or facts.
The principle of mathematical induction is one such tool which can be used to
prove a wide variety of mathematical statements. Each such statement is
assumed as P(n) associated with positive integer n, for which the correctness
for the case n = 1 is examined. Then assuming the truth of P(k) for some
positive integer k, the truth of P (k+1) is established.
Historical Note
Unlike other concepts and methods, proof by mathematical induction is not
the invention of a particular individual at a fixed moment. It is said that the principle
of mathematical induction was known by the Pythagoreans.
The French mathematician Blaise Pascal is credited with the origin of the
principle of mathematical induction.
The name induction was used by the English mathematician John Wallis.
Later the principle was employed to provide a proof of the binomial theorem.
De Morgan contributed many accomplishments in the field of mathematics
on many different subjects. He was the first person to define and name
“mathematical induction” and developed De Morgan’s rule to determine the
convergence of a mathematical series.
G. Peano undertook the task of deducing the properties of natural numbers
from a set of explicitly stated assumptions, now known as Peano’s axioms.The
principle of mathematical induction is a restatement of one of the Peano’s axioms.
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