How about a challenge? Think as few as you can! Hmmm... Did you think about the zero? If so, I need to tell you that there are some numbers that can be smaller than he is. Some don't, existinfinite numbersless than zero! And chances are, you've seen them around.
Whenever it's winter, temperatures drop. Some cities in southern Brazil even snow. When this happens, the temperature is less than zero. In Urupema, city of Santa Catarina, the temperature has already reached -6.8°C in the year 2013.
I will offer you a new challenge! This time it will be a quick question: “You have BRL 5.00 in your wallet, you lose a bet to your friend and you owe him BRL 8.00. After paying the bet, what will your situation be?” In this case, if you pay the BRL 5.00 to your friend, you will still owe him BRL 3.00. We can say that your balanceit's from – 3 real.
The negative numbers we mentioned, as well as all the other existing ones, belong to a numeric set very special called Set of Integers, which can be represented by the letter
. Integer numbers are made up of the natural numbers and also the negative numbers, in addition to the zero, which has no sign. We can represent this numerical set as follows:
= {…, – 3, – 2, – 1, 0, 1, 2, 3, …}.
This set is said to be positively infinite and negatively infinite, as it has infinitely many positive and negative numbers. Another way to visualize negative numbers is through the number line, as it manages to organize them efficiently, in addition to the fact that the line gives us the idea of infinity. On the number line, to the right of zero, are the natural (positive) numbers and, to the left of zero, are the negative numbers:
Representing whole numbers using the number line
There are some situations where it is not appropriate to use all whole numbers. For these cases, we have some special number sets and their representations:
Set of Non-null Integers (without the zero)
* = {…, – 3, – 2, – 1, 1, 2, 3, …}.
Set of Non-Negative Integers (zero and positive numbers)
+ = {0, 1, 2, 3, …}.
Positive Integer Set (only numbers greater than zero)
*+ = { 1, 2, 3, …}.
Set of Non-Positive Integers (zero and negative numbers)
– = {…, – 3, – 2, – 1, 0}.
Set of Negative Integers (only numbers less than zero)
*– = {…, – 3, – 2, – 1}.
By Amanda Gonçalves
Graduated in Mathematics
