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Notes on Algebraic Inequalities.—
Published online by Cambridge University Press: 31 October 2008
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It is worthy of remark that there is a method of proving algebraic inequalities which is very generally applicable, and which furnishes proofs of great directness and completeness.
The method consists in expressing the difference A – B in a manifestly positive form, when we have to prove A > B.
The first inequality occurring in school Algebra is usually proved in this way. We have to show that if a, b, and x are positive quantities is nearer to 1 than
. We have
The two cases a > b and b > a are then considered separately, and the conclusion drawn.
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- Copyright © Edinburgh Mathematical Society 1912