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INTRODUCTION
Any statement can be classified as general or particular. Examples of general statements are:
All citizens of the U.S.S.R. are entitled to an education.
The diagonals of a parallelogram bisect one another.
All numbers ending in zero are divisible by 5.
Examples of particular statements are:
Petrov is entitled to an education.
The diagonals of the parallelogram ABCD bisect one another.
140 is divisible by 5.
The process of deriving a particular statement from a general statement is called deduction. Consider these statements:
(1) All citizens of the U.S.S.R. are entitled to an education.
(2) Petrov is a citizen of the U.S.S.R
(3) Petrov is entitled to an education.
From general statement (1), together with particular statement (2), we obtain particular statement (3).
The process of obtaining general statements from particular statements is called induction. Inductive reasoning may lead to false as well as to true conclusions. We shall clarify this point by two examples.
First Example.
(1) 140 is divisible by 5.
(2) All numbers ending in zero are divisible by 5.
General statement (2), obtained from particular statement (1), is true.
Second Example.
(1) 140 is divisible by 5.
(2) All three-place numbers are divisible by 5.
In this case, general statement (2), derived from particular statement (1), is false.
How can induction be used in mathematics so that only true general statements are obtained from particular statements? The answer to this question is given in this booklet.
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Excerpted from "Induction in Geometry"
by .
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