An Introduction to the Logic of Algebra With Illustrative Exercises

Cover An Introduction to the Logic of Algebra With Illustrative Exercises
An Introduction to the Logic of Algebra With Illustrative Exercises
Ellery W Ellery Williams Davis
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i r - The condition becomes o < r — p — ra q -\- pa q, precisely what 1 we had before with r, /, and cfl in place of h, k, and a ; and is true because these numbers fulfil all the conditions imposed upon h y k, and a. a k — I a h — 1 •. — 7 — < — -j — for o < k < h 54 AN INTRODUCTION TO THE LOGIC OF ALGEBRA. when k and h are commensurable. But, since the values of the expression when k and h are incommensurable are hemmed in by the values when k and h are commensurable, the in- equality is always true, and there is no least value of Neither is there a greatest value of k a~ h — i This will be found to hang upon the inequality o t — for h > o and k > o, whether h > k, h = k, or h < k.

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