On the Infinite and the Infinitely Small

Euler

Chapter 3 in Foundations of Differential Calculus, 2000, pp 47-61 from Springer

Abstract: Abstract Since every quantity, no matter how large, can always be increased, and there is no obstacle to adding to a given quantity another like quantity, it follows that every quantity can be increased without limit. Furthermore, there is no quantity so large that a larger one cannot be conceived, and so there is no doubt that every quantity can be increased to infinity. If there is someone who would deny this, he would have to give some quantity that cannot be increased, and so he needs to give a quantity to which nothing can be added. This is absurd, and even the idea of quantity rules out this possibility. He must necessarily concede that every quantity can always be increased without limit, that is, it can be increased to infinity.

Keywords: Negative Number; Plane Curf; Divergent Series; Simple Part; Geometric Ratio (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/0-387-22645-1_3

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