# Arithmetic - Early Development Of Arithmetic, Numbering System, Axioms Of The Operations Of Arithmetic, Numbers And Their Properties

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addition multiplication

Arithmetic is a branch of **mathematics** concerned with the numerical manipulation of numbers using the operations of **addition**, **subtraction**, **multiplication**, **division**, and the extraction of roots. General arithmetic principles slowly developed over **time** from the principle of counting objects. Critical to the advancement of arithmetic was the development of a positional number system and a symbol to represent the quantity **zero**. All arithmetic knowledge is derived from the primary axioms of addition and multiplication. These axioms describe the rules which apply to all **real numbers**, including whole numbers, **integers**, rational, and irrational numbers.

## Additional Topics

Our numbering system is of central importance in the subject of arithmetic. The system we use today called the Hindu-Arabic system, was developed by the Hindu civilization of India some 1,500 years ago. It was brought to Europe during the middle ages by the Arabs and fully replaced the Roman numeral system during the seventeenth century. The Hindu-Arabic system is called a decimal system because i…

Arithmetic is the study of mathematics related to the manipulation of real numbers. The two fundamental properties of arithmetic are addition and multiplication. When two numbers are added together, the resulting number is called a sum. For example, 6 is the sum of 4 + 2. Similarly, when two numbers are multiplied, the resulting number is called the product. Both of these operations have a related…

These axioms apply to all real numbers. It is important to note that real numbers is the general class of all numbers that includes whole numbers, integers, rational numbers, and irrational numbers. For each of these number types only certain axioms apply. Whole numbers, also called natural numbers, include only numbers that are positive integers and zero. These numbers are typically the first one…

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