A number is a mathematical object used to count and measure. A notational symbol that represents a number is called a numeral but in common use, the word number can mean the abstract object, the symbol, or the word for the number. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (e.g., ISBNs). In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.
Certain procedures that take one or more numbers as input and produce a number as output are called numerical operations. Unary operations take a single input number and produce a single output number. For example, the successor operation adds one to an integer, thus the successor of 4 is 5. Binary operations take two input numbers and produce a single output number. Examples of binary operations include addition, subtraction, multiplication, division, and exponentiation. The study of numerical operations is called arithmetic.
The most familiar numbers are the natural numbers or counting numbers: one, two, three, and so on. Traditionally, the sequence of natural numbers started with 1 (0 was not even considered a number for the Ancient Greeks.) However, in the 19th century, set theorists and other mathematicians started including 0 (cardinality of the empty set, i.e. 0 elements, where 0 is thus the smallest cardinal number) in the set of natural numbers. Today, different mathematicians use the term to describe both sets, including zero or not. The mathematical symbol for the set of all natural numbers is N, also written .
In the base ten numeral system, in almost universal use today for arithmetic operations, the symbols for natural numbers are written using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In this base ten system, the rightmost digit of a natural number.