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

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.