Definition of "arithmetic"

Note that all correctly rounding arithmetics satisfy property A1, as do those with properly truncating addition. All faithful binary arithmetics and all arithmetics with either properly truncating or correctly chopping addition satisfy property A2.

1992, Douglas M. Priest, On Properties of Floating Point Arithmetics, University of California, Berkeley, page 17

[The researchers] noticed many of their pieces of [plastic marine] debris sported surface pits around two microns across. […] Closer examination showed that some of these pits did, indeed, contain bacteria, and that in several cases these bacteria were dividing and thus, by the perverse arithmetic of biological terminology, multiplying.

2013 July 20, “Welcome to the plastisphere”, in The Economist, volume 408, number 8845

Moreover, the latest work of Katz, involving the so-called 'Larsen alternative', provides new criteria, of a very arithmetic nature, to (almost) determine the rational monodromy group

2008, Emmanuel Kowalski, The large sieve and its applications: arithmetic geometry, random ..., page 189