Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 noun The mathematics of integers, rational numbers, real numbers, or complex numbers under addition, subtraction, multiplication, and division.
 adjective Of or relating to arithmetic.
 adjective Changing according to an arithmetic progression.
from The Century Dictionary.
 noun The theory of numbers; the study of the divisibility of whole numbers, the remainders after division, etc. Also called
theoretical or higher arithmetic.  noun The art of computation: the most elementary branch of mathematics.
 noun (pron. arithmet′ ik). An arithmetician.
 noun etc. See the adjectives.
 A less common form of
arithmetical .
from the GNU version of the Collaborative International Dictionary of English.
 noun The science of numbers; the art of computation by figures.
 noun A book containing the principles of this science.
 noun trigonometry.
 noun the application of the science of numbers to problems in civil government, political economy, and social science.
 noun the name given by Sir Isaac Newton to algebra.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun The
mathematics ofnumbers (integers ,rational numbers ,real numbers , orcomplex numbers ) under theoperations ofaddition ,subtraction ,multiplication , anddivision .  adjective mathematics Of, relating to, or using arithmetic;
arithmetical .  adjective arithmetic Of a
progression ,mean , etc, computed using addition rather than multiplication.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adjective relating to or involving arithmetic
 noun the branch of pure mathematics dealing with the theory of numerical calculations
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
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Examples

Hollyhock sat down to the midday meal at The Garden in exceedingly low spirits, but her father had now got through what she called his arithmetic, and was full of mirth.
Hollyhock A Spirit of Mischief L. T. Meade 1884

But that kind of arithmetic is not from the Spirit.

He needs to crawl back under the rock he came out from under. arithmetic is liberal

In that proof, the expressive power of arithmetic is needed to get selfreference and incompleteness.

I think you may have just proved that arithmetic is indeed liberal.

That road you use to drive to your klan meetings was probably paid for with CA dollars .... show some respect. arithmetic is liberal

In that proof, the expressive power of arithmetic is needed to get selfreference and incompleteness.

The use of Peano arithmetic is fairly pervasive in mathematical physics, hence, at first sight, this appears to be highly damaging to the prospects for a final Theory of Everything in physics.
Archive 20090601 Gordon McCabe 2009

Hopeless cnn you are part of it ...!!!!!!!!!! arithmetic is liberal

Moreover, whilst Peano arithmetic is axiomatizable, there is a particular model of Peano arithmetic, whose theory is typically referred to as Number theory, which Godel demonstrated to be undecidable and nonaxiomatizable.
Archive 20090601 Gordon McCabe 2009
wiredweird commented on the word arithmetic
(uhRITHmuhTick) numerical manipulations
(AirithMETick) adj, pertaining to mathematical operations
March 27, 2007
asativum commented on the word arithmetic
Including, the Mock Turtle tells us, ambition, distraction, uglification and derision.
October 1, 2008