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

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.

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

The first page of this text:

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

Index to Mathematical Treasures