In mathematics, numbers are objects used to count, label, and measure. In mathematics, the definition of a number has been extended  throughout history to include such numbers as 0, negative numbers, rational numbers, irrational numbers, real numbers, and complex numbers.

Mathematical operations are certain procedures that take one or more numbers as input and produce a number as output. Unary operations take a single input number and produce a single output number. For example, the successor operation adds 1 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.

A notational symbol that represents a number is called a numeral. 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 common usage, the word number can mean the abstract object, the symbol, or the word for the number.

source, adapted from