Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence
calculation, division, factorization, multiplication,
power computation, root extraction, and subtraction.
Arithmetic was part of the quadrivium
taught in medieval universities. A mnemonic for the spelling of "arithmetic"
is "a rat in the house may eat the ice cream."
The branch of mathematics known as number theory is sometimes known as higher
arithmetic.
Modular arithmetic is the
arithmetic of congruences.
Floating-point arithmetic is the arithmetic performed on real numbers by computers or other automated devices
using a fixed number of bits.
The fundamental theorem of arithmetic, also called the unique factorization theorem, states that
any positive integer can be
represented in exactly one way as
a product of primes.
The Löwenheim-Skolem theorem, which is a fundamental result in model
theory, establishes the existence of "nonstandard" models of arithmetic.
Portions of this entry contributed by Lynda Sherman
Derbyshire, J. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem
in Mathematics. New York: Penguin, pp. 371-372, 2004.
Karpinski, L. C. The History of Arithmetic. Chicago, IL: Rand, McNally,
& Co., 1925.
Maxfield, J. E. and Maxfield, M. W. Abstract Algebra and Solution by Radicals. Philadelphia,
PA: Saunders, 1992.
Thompson, J. E. Arithmetic for the Practical Man. New York: Van Nostrand
Reinhold, 1973.
Weisstein, E. W. "Books about Arithmetic." http://www.ericweisstein.com/encyclopedias/books/Arithmetic.html.
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