Abstract
THE subject of this tract has been hitherto inaccessible to English readers, and it is not altogether easy to give a brief account of its contents. Perhaps the simplest method is to start from the familiar facts that log x and ex both tend to infinity with x, but in very different ways, namely, (log x)/xδ tends to zero, however small δ may be, and ex/xδ tends to infinity, however large δ may be (it is understood that δ, δ do not vary with x). These results would be expressed in du Bois-Reymond's notation by the symbols
Orders of Infinity: the "Infinitärcalcül" of Paul du Bois-Reymond.
By G. H. Hardy Pp. iv + 62. (Cambridge: University Press, 1910.) Price 2s. 6d. net.
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B., T. Orders of Infinity: the “ Infinitärcalcül ” of Paul du Bois-Reymond . Nature 86, 307 (1911). https://doi.org/10.1038/086307a0
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DOI: https://doi.org/10.1038/086307a0