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Maths > Integers > Introduction to Integers
Integers

Introduction to Integers

Today we are going to introduce ourselves to a unique idea in maths. It is called an ‘Integer’. What is an integer? Let’s suppose a farmer has 17 sheep and all but 9 of them die. So how many does he have left now? Yes, 9! This is actually the idea that we shall discuss here. Let’s understand what is an integer. Let us first understand the basics of integer here.

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What are the Numbers?

Any number is a symbol we use to denote a quantity are numbers. For example,  2, 5, 99 etc. Now, numbers are classified into various types:

 

What is an integer

 

I. Natural Numbers

Numbers used for counting in everyday life are called natural numbers eg. 2 pens, 6 chocolates etc. The addition of 2 natural numbers is a natural number, for example, 2 + 3 = 5. Also, the multiplication of 2 natural numbers is a natural number. For example, 2 × 3 = 6.

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II. Whole Numbers

All natural numbers along with zero (0) are called whole numbers. Therefore zero (0) is not a natural number as you cannot count zero. But zero is a whole number. Thus every natural number is a whole number. Zero is the only whole number that is not a natural number.

Addition of 2 whole number is a whole number, for example, 4 + 0 = 4. Also, the multiplication of 2 whole numbers is also a whole number, for example, 4 × 0 = 0.

III. Negative Numbers

Negative numbers are a concept i.e. they do not exist in reality. But for the purpose of calculation, we imagine a number system in which all natural numbers are preceded by a negative sign, for example, -1, -2, -3, -4….and so on. Their value is less than 0 and as the numbers increase the value of the unit decreases, for example -1 > -2> -3> -4> -99 >-20000  and so on.

The addition of 2 negative numbers is also a negative number, for example (-2) +(-4) = (-6). Also the subtraction of a negative number may or may not be a negative number, for example (-2) -(-4) =-2 +4 = 2.

Multiplication/ division of 2 negative numbers is a positive number, for example -2 × -4 = 8;  -4 /-2 = 2. With these concepts clear, we now proceed to the main topic of our discussion.

What is an Integer?

An integer is any number which is included in a set of combination of all the above numbers types. i.e. if we construct a set of all natural numbers, whole numbers, and negative numbers then such a set is called an Integer set, it can be represented as,

(……-3, -2, -1, 0, 1, 2, 3, ……)

So, every natural number is an integer, every whole number is an integer, and every negative number is an integer. The sum of 2 or more integers is an integer, for example, 2 + 4+ (-2) = 4. Also, the subtraction of 2 integers is also an integer, for example 2 + (-4) = -2. Similarly, the multiplication of 2 integers is also an integer, for example, 2 × -4 = -8.

The set of integers does not include fractions i.e p/q form or numbers which are in decimals eg: 2.4, 3.2 etc. The set of integers is an infinite set which means it has no ending on either side. That is because for every number on either the positive or negative side there is always one another number at an increment or decrement of 1 respectively. Hence the set of integers cannot be bound and is thus inexhaustible.

Solved Question for You

Question 1: Find 2 consecutive numbers whose sum is 129

Answer: Assume the numbers are ‘x’ and ‘x+1’

x + x + 1 = 129
so, 2x = 129 – 1
2x = 128
x = 64
if x = 64 then, x+1 = 65.
Hence, the numbers are 64 and 65.

This concludes our discussion on the topic – what is an integer.

Question 2: Explain what is an integer with examples?

Answer: It refers to a whole number that can be positive, zero, or negative. But, integers cannot be fractions or in decimals, they need to be the whole number. For instance, -7, -3, -2, 0 , 5, 7, 10, 2015, etc. Some examples of non-integers are ¼, 7.52, 0.05, 58/36, etc.

Question 3: What is the use of integer in daily life?

Answer: In our daily life, there are many uses of integers such as they help in computing the efficiency in positive or negative numbers in almost every field. In addition, they help to know the position where one is standing. And most importantly, it helps to calculate how more or fewer measures to be taken for achieving better results.

Question 4: Is zero an even number?

Answer: Yes, zero is an even number because we can easily verify it based on the definition of even that is even numbers are those integers that are multiples of 2. So, when we multiply 0 with 2 then the answer is 0 in this sense 0 is an even number.

Question 5: What is the importance of integers?

Answer: They are important because they help to facilitate certain calculations by including negative numbers. In addition, they also include all negative and positive numbers without a decimal point.

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