Mathematicians categorized numbers into different types that include prime numbers, natural numbers, whole numbers, and many more. One of them is Integers. These types help us a lot in different maths problems. Integers and natural numbers are very close but they have one big difference. In the case of natural numbers, it is not possible to operate when the minuend is smaller than the subtrahend, but in life, there are such operations. For example, the need to represent owed money, temperature below zero, and depths with respect to sea level.

In simple words, natural numbers don't consider negative entities and that is where integers come to play. The previous examples require us to expand the concept of natural numbers and introduce a new numerical set called integers. Integers work with both entities, meaning that integers can be positive or negative.

A set of integers is formed by:

Z=\{ ...-5,-4,-3,-2,-1,0,1,2,3,4,5...\}

Let's compare integers with natural numbers to find the relation. If you looked carefully, you can actually see natural numbers. From 0 to infinity, all those numbers are natural numbers. This means that all natural numbers can be integers but all integers can't be natural numbers. However, they have something in common, they both don't exist in decimal or in fractions. The reason is that decimal numbers and fractions are called irrational numbers which is a whole new topic, let's stick to integers for now. In conclusion, integers include all the negative whole numbers and all natural numbers. Integers also have categories of their own. There are three types of integers. The first one is the positive integers, the second one is the negative integers, and last but not least is zero.

Z\quad =\quad { Z }^{ - }U\{ 0\} U{ Z }^{ + }

Since we know that integers contain positive integers, this means natural numbers are a subset of integers.

N\subset Z

 

Absolute Value of an Integer

Sometimes, we don't require the direction of a number. In easy words, we are looking for the magnitude of that number. Finding the magnitude of an integer is very easy. All you need to do is to find the absolute value of that number and to do that, you need modulus. Modulus is a mathematical operation that extracts the absolute value of any integer. Basically, modulus removes the sign of the integer hence providing the absolute value. The absolute values are written between vertical bars.

\left| -5 \right| = 5

\left| 5 \right| = 5

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Representation of Integers

Of course, there is a different way to represent integers otherwise many people will get confused between integers and natural numbers. Below are the steps to represent integers.

  1. Draw a horizontal line and divide it into equal parts from the midpoint of the line.
  2. That midpoint is your zero. Write zero below the line.
  3. On your right, start writing positive integers.
  4. On your left, start writing negative integers.
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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.