Real number system
Natural numbers
The set of numbers which are used for
counting is called natural numbers. In other words, the set of natural numbers
consists 1 and each natural numbers has a successor n + 1. It is denoted by N
or Z+.
Integers
A number is said to be a member of set
of integers, if it consists positive natural number and negative of natural
numbers with zero. It is denoted by Z or I.
Rational numbers
A number is said to a rational number
if it can be expressed as m/n where n ¹ 0 and m, n Î Z. A set
of rational number is denoted by Q.
Irrational numbers
A real number which is not rational
(it cannot be expressed as ) is called an irrational number. A
set of irrational number is denoted by R - Q or Ir, where Q denotes
the set of rational numbers and R denotes as universal set of real numbers.
Real numbers
A set of numbers which consists of all
set of rational and the set of irrational numbers is called the set of real
numbers. It is denoted by R.
Interval
Let a and b be two numbers on the real
line. Then the set of points on the real line between a and b is known as an
interval. The real numbers a and b are known as the end points of the interval.
An interval not containing the end points a and b is known as open interval.
The open interval is denoted by (a, b).
In symbol, (a, b) = {x: a < x < b}
An interval containing both the end
points a and b is known as the closed interval and it is denoted by [a, b]. In
symbol, [a, b] = {x: a £ x £ b}.
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