**Integer Formula (Table of Contents)**

## Integer Formula

Any number which can be written without any fractions is known as an integer. So, integers are basically whole numbers which can be positive, zero or negative but no fractions. A set of integers is denoted by Z, which can be written as Z = {…-5,-4,-3,-2,-1, 0, 1, 2, 3, 4, 5…….}. Here Z is a set which has a property of Denumerability which basically tells us that although there is an infinite number of elements in Z, those values are countable and can be identified in the set. The real number includes all the number including fractions also and real number can be converted into integers by rounding the number to the nearest integer. For example, 1, 34, 9890, 340945, etc. all are integers and 9.4, 34.56, 803.45 are a real number which can be rounded off to 9, 35, and 803 which are integers.

Formula For Integer:

There is no particular formula for integer as it is nothing but a set of numbers. But there are certain rules when we perform any mathematical operations like addition, subtraction, etc on integers:

- Adding two positive integers will always result in a positive integer.
- Adding two negative integers will always result in a negative integer.
- Adding one positive and one negative integer will result in
- Positive number if a positive integer is greater
- Negative number if a negative integer is greater

**Examples of Integer Formula**

Let’s take an example to understand the calculation of Integer formula in a better manner.

#### Integer Formula – Example #1

**Let’s say we have a set of integers and is given by Z = {2,3,-3,-4,9}**

**Solution:**

Let’s try to understand the rules which we discussed above.

**Adding two positive integers will always result in a positive integer.**

So let’s take 2 positive integers from the set: 2, 9.

So 2+9 = 11 which is a positive integer.

**Adding two negative integers will always result in a negative integer.**

So let’s take 2 negative integers from the set: -3, -4.

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So -3-4 = -7 which is a negative integer.

**Adding one positive and one negative integer will result in**

1. Positive number if a positive integer is greater.

So let’s take one positive and one negative integer from the set: -3, 9.

So -3+9 = 6 which is a positive integer.

2. Negative number if a negative integer is greater.

So let’s take one positive and one negative integer from the set: -3, 2.

So -3+2 = -1 which is a negative integer.

#### Integer Formula – Example #2

**Let say you are performing some mathematical equation where you know that sum of two consecutive integers is given by 97. Now you want to find out what are those numbers.**

**Solution:**

Assume that the 1^{st} integer is x.

The 2^{nd} integer will be x + 1.

So,

- x + (x + 1) = 97
- 2x + 1 = 97
- 2x = 97 – 1
- 2x = 96
- x = 96 / 2
- x = 48

So, the 1^{st} integer is **48**

and 2^{nd} integer is 48 + 1 = **49**

### Explanation

Integer, as explained above is basically a set of number which contains all numbers except fractional numbers. Integers can be positive or negative, even 0 is also an integer. Also, as we have seen in the above examples, addition, subtraction, and multiplication of two or more integers will always result in integer but this is not the case with division function. Using division can result in an integer or a fraction. For example, if we divide 10 by 2, we will get 5 which is an integer but if 10 is divided by 4, then it is 2.5 which is not an integer.

### Relevance and Uses of Integer Formula

Integers are used in programming languages and coding because these systems only understand binary numbers i.e, 1 or 0. So everything or anything a computer system does, it converts it into binary numbers first. Integers are used in mathematics, finance, statistical tools, etc. Basically, they are the core element of all these fields. Integers are really important not in statistical tools and mathematical operations but in real life also. If you want to count how much money you have in your wallet that is an integer. If you want to count how many students in the class, again an integer. A number of trees in your backyard, the number of cars you have, the number of years of experience you have, etc, all are integers. So the intensity integers in real life are so large and it cannot be measured. In a single line, we can say that integers are everywhere.

### Recommended Articles

This has been a guide to Integer Formula. Here we discuss How to Calculate Integer along with practical examples. You may also look at the following articles to learn more –