number theory (higher arithmetic)

Number theory, also known as higher arithmetic, is a branch of mathematics concerned with the properties of integer s, rational number s, irrational number s, and real number s. Sometimes the discipline is considered to include the imaginary and complex numbers as well.

Formally, numbers are represented in terms of set s; there are various schemes for doing this. However, there are other ways to represent numbers -- for example, as angles, as points on a line, as points on a plane, or as points in space.

The integers and rational numbers can be symbolized and completely defined by numeral s. The system of numeration commonly used today was developed from systems used in Arab texts, although some scholars believe they were first used in India. The so-called Arabic numerals are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.