A number is a mathematical object used to count and measure. A notational symbol that represents a number is called a 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 operation (mathematics)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. More common are binary operations, which 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.
Classification of numbers Edit
Different types of numbers are used in different cases. Numbers can be classified into sets, called number systems.
Natural | 1, 2, 3, 4, 5, 6, 7, ..., n |
---|---|
Integers | −n, ..., −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, ..., n |
Positive integers | 1, 2, 3, 4, 5, ..., n |
Rational | ^{a}⁄_{b} where a and b are integers and b is not zero |
Real | The limit of a convergent sequence of rational numbers |
Complex | a + bi where a and b are real numbers and i is the square root of −1 |