Few days ago I wrote an article about Real Number System here. There I explained the real number system starting from Natural Numbers till Irrational Numbers. Today's topic is all about Integers and without learning about Integers one can't pass Grade 6 maths standards all around the world.
So let's dig integers a little deeper:
Integers are the group of numbers which includes natural numbers (1, 2, 3, 4....), zero and negative numbers below zero. We need Integers because whole numbers can't help us when we have to count below zero.
For example; in winter the temperatures go below zero in many parts of the world. Some buildings have parking floors underground, if ground level is zero, what number can be given to these underground levels?
Normally height of mountains or other higher regions is calculated considering the sea surface level at zero. What about the depth which is below the sea surface level?
Our bank accounts normally have some money we deposited, and if we withdraw all of it from our account, the account balance becomes zero. What if we have an overdraft limit and we overdrawn our bank account?
So, there are a lots of more examples in our daily lives where whole numbers are not helpful. Therefore mathematicians found another set of the numbers and name this set the Integers.
The negative numbers are the additive inverse (negative of a Natural number and when added to the number gives zero) of the Natural numbers. For example the additive inverse of 1 is –1, so that, 1-1 = 0 or additive inverse of 2 is –2 and so on.
The integers are represented by the symbol “I” or “Z”.
I = ………… -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ………...
Notice that number 0 is neither positive nor negative and is called the neutral integer. Right side to zero is the positive integers (or the natural numbers) and left side to zero are negative integers.
Also notice that positive sign is not shown in front of any of the positive integers, so remember that any number without a sign actually has a positive sign in front of it and which need not to be shown, as this is understood in math all over the world. Remember, 2 is actually +2 or 3 is +3 and same for every other positive integer.