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Mathematical Treasure: G. H. Hardy's Orders of Infinity

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

At the turn of the nineteenth-century, much attention was focused on the foundations of real analysis. One of the issues considered was the idea of a function approaching infinity as a limit: 'How does it behave?' 'Does it diverge rapidly or slowly?' A “scale of measurement” determining “orders of infinity” was devised to describe this process. (For a further discussion, see the article Math Origins: Orders of Growth here in Convergence.) In 1910, G. H. Hardy (1877-1947) published Orders of Infinity, subtitled The 'Infinitärcalcül' of Paul Du Bois-Reymond. The work examined the "infinitary calculus" or behavior at infinity of real-valued functions.

Title page of Orders of Infinity by G. H. Hardy, 1910

In his “Preface,” Hardy referenced the work of the German mathematician Paul du Bois-Reymond:

Preface of Orders of Infinity by G. H. Hardy, 1910

The first page of this text:

First page of Orders of Infinity by G. H. Hardy, 1910

The full work, from the University of Toronto, can be viewed in the Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: G. H. Hardy's Orders of Infinity," Convergence (February 2019)

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