According to a narrow characterization, arithmetic deals only with natural numbers. There are disagreements about its precise definition. The term "arithmetic" has its root in the Latin term " arithmetica" which derives from the Ancient Greek words ἀριθμός (arithmos), meaning "number", and ἀριθμητική τέχνη (arithmetike tekhne), meaning "the art of counting". ![]() In a wider sense, it also includes exponentiation, extraction of roots, and logarithm. In particular, it deals with numerical calculations using the arithmetic operations of addition, subtraction, multiplication, and division. In the 20th century, the emergence of electronic calculators and computers revolutionized the accuracy and speed with which arithmetic calculations could be performed.ĭefinition, etymology, and related fields Īrithmetic is the fundamental branch of mathematics that studies numbers and their operations. The 18th and 19th centuries saw the development of modern number theory and the formulation of axiomatic foundations of arithmetic. The first mechanical calculators were invented in the 17th century. ![]() The ancient Indians developed the concept of zero and the decimal system, which Arab mathematicians further refined and spread to the Western world during the medieval period. Starting in the 7th and 6th centuries BCE, the ancient Greeks initiated a more abstract study of numbers and introduced the method of rigorous mathematical proofs. Ancient civilizations like the Egyptians and the Sumerians invented numeral systems to solve practical arithmetic problems in about 3000 BCE. The practice of arithmetic is at least thousands and possibly tens of thousands of years old. Its cognitive and conceptual foundations are studied by psychology and philosophy. It is one of the earliest forms of mathematics education that students encounter. ![]() Arithmetic is present in many aspects of daily life, for example, to calculate change while shopping or to manage personal finances. They play a similar role in the sciences, like physics and economics. Some arithmetic systems operate on mathematical objects other than numbers, such as interval arithmetic and matrix arithmetic.Īrithmetic operations form the basis of many branches of mathematics, such as algebra, calculus, and statistics. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Another distinction is based on the numeral system employed to perform calculations. Real arithmetic includes calculations with both rational and irrational numbers and covers the complete number line. Rational arithmetic includes operations on fractions that lie between integers. Integer arithmetic restricts itself to calculations with positive and negative whole numbers. Arithmetic systems can be distinguished based on the type of number they operate on. ![]() In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Elementary branch of mathematics The main arithmetic operations are addition, subtraction, multiplication, and division.Īrithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division.
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