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.

Early development of arithmetic

Arithmetic developed slowly over the course of human history, primarily evolving from the operation of counting. Prior to 4000 b.c., few civilizations were even able to count up to ten. Over time however, people learned to associate objects with numbers. They also learned to think about numbers as abstract ideas. They...