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# Are all counting numbers Integers?

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, labelling, 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’.

### Are all counting numbers Integers?

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

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,………….

The number with no decimal or fractional part from the set of negative and positive numbers, including zero.

Examples of integers are: -8, -7, -5, 0, 1, 5, 8, 97, and 3,043.

Types of Integers

Two types of integers are:

Positive Integers: The integer number is positive if it is greater than zero.

Example: 1, 2, 3, 4,…

Negative Integers: The integer number is negative if it is less than zero. Example: -1, -2, -3, -4,… and here Zero is defined as neither negative nor positive integer. It is a whole number.

Z = {… -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, …}

So the answer to the above question is NO all counting numbers are not integers as it doesnot include negative numbers and zero.

### Sample Questions

Question 1: Identify from below which are counting numbers?

6, 0, 8.008, 5/7, 2

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 2: Is 16 a counting number or integer?

Counting numbers or Natural numbers are the positive numbers that count from 1 to infinity.

Therefore, 16 being a positive number is a counting number as well as integer.

Question 3: What are the smallest four-digit and largest four-digit counting 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.

Smallest four digit counting number is 1000

Largest four digit counting number is 9999

Question 4: From these below numbers, which are integer as well as counting numbers?

5/4, 4.55, 45454/123, -1, -5, -78,1, 23, 128