The number system includes different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures as well as words accordingly. For example, the numbers like 40 and 65 expressed in the form of figures can also be written as forty and sixty-five.
A Number system or numeral system is defined as an elementary system to express numbers and figures. It is the unique way of representing of numbers in arithmetic and algebraic structure.
Numbers are used in various arithmetic values applicable to carry out various arithmetic operations like addition, subtraction, multiplication, etc which are applicable in daily lives for the purpose of calculation. The value of a number is determined by the digit, its place value in the number, and the base of the number system. Numbers generally are also known as numerals are the mathematical values used for counting, measurements, labeling, and measuring fundamental quantities.
Numbers are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 2, 4, 7, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.
Types Of Numbers
There are different types of numbers categorized into sets by the number system. The types are described below,
- Natural numbers: Natural numbers are the positive numbers that count from 1 to infinity. The set of natural numbers is represented by ‘N’. It is the numbers we generally use for counting. The set of natural numbers can be represented as N = 1, 2, 3, 4, 5, 6, 7,…
- Whole numbers: Whole numbers are positive numbers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is represented by ‘W’. The set can be represented as W = 0, 1, 2, 3, 4, 5,…
- Integers: Integers are the set of numbers including all the positive counting numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The set of integers is denoted by ‘Z’. The set of integers can be represented as Z = …..,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,…
- Decimal numbers: Any numeral value that consists of a decimal point is a decimal number. It can be expressed as 2.5, 0.567, etc.
- Real number: Real numbers are the set numbers that do not include any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by ‘R’.
- Complex number: Complex numbers are a set of numbers that include imaginary numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
- Rational numbers: Rational numbers are the numbers that can be expressed as the ratio of two integers. It includes all the integers and can be expressed in terms of fractions or decimals. It is denoted by ‘Q’.
- Irrational numbers: Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point. It is denoted by ‘P’.
What is the difference between counting numbers and whole numbers?
Whole numbers
The subset of the number system that consists of all positive integers including 0 is defined as a whole number. The whole number counts from zero to positive infinity. These numbers are mostly used for counting, measurement of fundamental quantities, and daily calculations.
Whole numbers are the only constituents of natural numbers including zero. The subset is given by {0,1,2,3,4,5,……….}, the set does not include fractions, decimals, and negative integers.
Examples of Whole Numbers
Positive integers also known as counting numbers including zero are the part of whole numbers, such as 0,1,2,3,4,5, etc, excluding negative integers, fractions, and decimals.
12, 120, 1200, etc all are examples of whole numbers.
332 is a whole number as it’s a positive integer
-214 is not a whole number as it’s not a positive integer
2.23 is not a whole number as it’s a decimal value
3/15 is not a whole number as it’s a fraction
Counting numbers
Counting numbers are nothing but natural numbers. Let’s learn in more detail about natural numbers,
Counting numbers or Natural numbers are the positive numbers that count from 1 to infinity. The set of natural numbers is represented by ‘N’. It is the numbers we generally use for counting. The set of natural numbers can be represented as N = 1, 2, 3, 4, 5, 6, 7,…
The other name for natural numbers is counting numbers as one can count the natural numbers with the use of hands. The natural numbers form a part of the number system which is positive integers from 1 onwards. These numbers are represented on the right side of a number line.
The example of natural numbers is 1, 2, 3, 4, 5,… N. Zero and negative integers are not a part of natural numbers.
The smallest natural number ever possible is 1 and the largest natural number can be any infinite positive integer value. Fractions, decimal values, complex numbers, etc are not natural numbers.
The set of numbers that we used to count anything is defined as counting numbers. All-natural numbers are counting numbers. And these numbers are always positive.
Examples are 1, 2, 3, 4, 5, … etc. and it doesn’t include zero .
33 is a natural number as it’s a positive integer
-24 is not a natural number as it’s not a positive integer
2.3 is not a natural number as it’s a decimal value.
3/5 is not a natural number as it’s a fraction
Difference between counting numbers and whole numbers:
|
Counting numbers |
Whole numbers |
| The set of counting numbers is {1,2,…N} | The set of Whole numbers is {0,1,2,…N} |
| The smallest counting number we have is 1 as it does not include zero | The smallest whole number is 0 |
| All non zero positive integers are a part of counting numbers | All positive integers are a part of whole numbers |
| A counting number is a subset of the Whole number | The whole number is a superset of natural number |
| Counting numbers are represented by the letter N | Whole numbers are represented by the letter W |
Sample Questions
Question 1: Are the numbers 200, 399, 457 whole numbers?
Answer:
Yes, the numbers 200, 399, 457 are the whole numbers.
Question 2: Identify from below which are counting numbers?
6, 0, 8.008, 5/7, 4
Answer:
The set of numbers that we used to count anything is defined as counting numbers. All-natural numbers are counting numbers. And these numbers are always positive. and counting number doesn’t include fraction and decimals and doesnot include zero
Here 6, 4 are the counting numbers.
Question 3: What are the counting as well as the whole number?
6, 14, 0, 8.008, 5/7, 888
Answer:
A counting number is a subset of the Whole number whereas The whole number is a superset of natural number.
both counting number and whole numbers does not include fractional or decimal value so here 6, 14, 888 are the counting as well as the whole number