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Note on the Fundamental Inequality Theorems connected with ex and xm
Published online by Cambridge University Press: 20 January 2009
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The subject of this note is that dealt with in Mr Tweedie's paper in the Proceedings, vol. XVII., 33–37, and my only reason for bringing it before the Society is to call attention to a slightly different method of presenting the same order of ideas. The method is that adopted by Peano, Lezioni di Analisi Infinitesimale, vol. I., §23, but as the book is not readily accessible to teachers, there may be some interest in having the method reproduced in our Proceedings. I add one or two remarks.
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- Copyright © Edinburgh Mathematical Society 1900
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* The reason for writing ex as the function of x which lies between (1 + x/m)m and (1−x/n)−n is that
where M = mx. The inequalities hold whether x be positive or negative, but m, n must be positive.
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