In this page we are going to discuss about types of numbers concept.In mathematics there are many number, among them few are natural numbers, whole numbers, integers, rational numbers. A number is also called as mathematical object which is used to count and measure. A notational symbol that represents a number is called a numeral but in a common use, the word number can be mean the abstract object, the symbol, or the word for a number.
Types of Numbers
In the number system, there are different types of numbers. Below are the types of numbers provided for your better understanding:
Natural Numbers:
The numbers 1, 2, 3… are called natural numbers. They are also called counting numbers since they are used for counting objects.
Whole Numbers:
The numbers 0, 1, 2 … are called whole numbers. The letter W denotes the collection of all whole numbers. We observe that W = {0, 1, 2…}
Now the equations such as x + 5 = 5 and x + 9 = 9 have solutions in W. We note that all natural numbers are whole numbers but there is the whole number 0, which is not a natural number.
Integers:
The numbers 0, 1, ?1, 2, ?2, … are called integers of which 1, 2, 3, … are called positive integers and ?1, ?2, ?3,… are called negative integers.
Rational Numbers:
A number of the form p/q where p and q are integers and q ? 0 is called a rational number. Q denotes the collection of all rational numbers. A rational number p/q is said to be in the proper form if q is a positive integer and p and q have no common factor other than 1.
Properties of Numbers
Following are the properties of numbers in the number system :
If x, y are rational numbers, then x+y is also a rational number. This property is called the closure property with respect to addition in Q.
If x, y are rational numbers, then x+y = y+x. This property is called the commutative property with respect to addition in Q.
If x, y, z are rational numbers, then x + (y + z) = (x + y) + z. This property is called the associative property of addition in Q.
The number 0 is a rational number and 0 + x = x + 0 = x for all rational number x. The rational number 0 is called the additive identity in Q.
For every rational number x, there is a rational number ?x such that x + (?x) = (?x) + x = 0. The rational number –x is called the negative of x or the additive inverse of x in Q
Types of Numbers
In the number system, there are different types of numbers. Below are the types of numbers provided for your better understanding:
Natural Numbers:
The numbers 1, 2, 3… are called natural numbers. They are also called counting numbers since they are used for counting objects.
Whole Numbers:
The numbers 0, 1, 2 … are called whole numbers. The letter W denotes the collection of all whole numbers. We observe that W = {0, 1, 2…}
Now the equations such as x + 5 = 5 and x + 9 = 9 have solutions in W. We note that all natural numbers are whole numbers but there is the whole number 0, which is not a natural number.
Integers:
The numbers 0, 1, ?1, 2, ?2, … are called integers of which 1, 2, 3, … are called positive integers and ?1, ?2, ?3,… are called negative integers.
Rational Numbers:
A number of the form p/q where p and q are integers and q ? 0 is called a rational number. Q denotes the collection of all rational numbers. A rational number p/q is said to be in the proper form if q is a positive integer and p and q have no common factor other than 1.
Properties of Numbers
Following are the properties of numbers in the number system :
If x, y are rational numbers, then x+y is also a rational number. This property is called the closure property with respect to addition in Q.
If x, y are rational numbers, then x+y = y+x. This property is called the commutative property with respect to addition in Q.
If x, y, z are rational numbers, then x + (y + z) = (x + y) + z. This property is called the associative property of addition in Q.
The number 0 is a rational number and 0 + x = x + 0 = x for all rational number x. The rational number 0 is called the additive identity in Q.
For every rational number x, there is a rational number ?x such that x + (?x) = (?x) + x = 0. The rational number –x is called the negative of x or the additive inverse of x in Q
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