arithmetic

arithmetic branch of mathematics commonly considered a separate branch but in actuality a part of algebra . Conventionally the term has been most widely applied to simple teaching of the skills of dealing with Numbers for practical purposes, e.g., computation of areas, proportions, costs, and the like. The four fundamental operations of this study are addition, subtraction, multiplication, and division. In advanced study the concept of number is greatly generalized to include not only complex numbers, but also quaternions, tensors, and abstract entities with no other meaning than that they obey certain laws (see algebra ). The division of arithmetic into the practical and the theoretical dates back to classical Greek times, when the term logistic referred to elementary arithmetic and the term arithmetic was reserved for the theory.

arithmetic Calculations and reckoning using numbers and operations such as addition, subtraction, multiplication and division. The study of arithmetic traditionally involved learning procedures for operations such as long division and extraction of square roots. The procedures of arithmetic were put on a formal axiomatic basis by Guiseppe Peano in the late 19th century. Using certain postulates, including that there is a unique natural number, 1, it is possible to give formal definition of the set of natural numbers and the arithmetical operations. Thus, addition is interpretable in terms of combining sets: in 2 + 7 = 9, 9 is the cardinal number of a set produced by combining sets of 2 and 7.