The Whole Numbers... A Lot of Talk About, Well, Nothing!

We have already learned about the counting numbers, those that come naturally to us when quantifying the world, but the minute we tried to subtract one number from itself we were struck by a number not in our set: the number ZERO.

You see, when we, as children, first learned about the counting numbers, we were always counting stuff - there was something there and we just wanted to quantify (tell how much) how much stuff was there. We never looked at the air and asked ourselves, How much is there?

How many birds are left after the two birds fly away?

However, at this point of our lives, when we are asking questions like this, we have finally come passed the world of just counting. Now we are starting to do cool things like adding and subtracting which, eventually leads us to the topic of having nothing!

A Daze-y Definition

Zero, the number, stands for the quantity of nothing.  Symbol: 0 
***NOTE: Zero plays another extremely important role in our number system - it is also a "place holder", like in the number 104. We will discuss THAT definition and role of zero in another post. This post is just about nothing!***

To answer the question above, we would say There are zero birds left because there are NO BIRDS. This may seem like a very long explanation over nothing, zero, nada, zilch - something you already understand, but I think it is really important to know that this was not an easy idea for people to think about. Some ancient civilizations didn't believe in zero, they felt there was no need to assign a number to nothing... that is an interesting thing to think about. How different would our math system be without using zero to represent nothing?

Thankfully (I think), we have a zero to work with and when we add that number to all of the other numbers we already know about in the set of counting numbers, then we have a whole new set of numbers, called The Whole Numbers.

A Daze-y Definition

The set of whole numbers includes zero, followed by all of the counting or natural numbers. We would write this set as {0, 1, 2, 3, 4, 5, 6...}.

Often when we begin to discuss multiple sets of numbers, we start building a visual graphic organizer, so we can see how the numbers relate to one another.

This shows us that ALL Natural numbers are Whole numbers because the Natural numbers are inside the red rectangle!

So, there you have it! A whole lot of talk about NOTHING! It is important to know the difference between these two sets of numbers and it is also really important to realize, even for just a moment, how big of a deal zero is! We will look at zero a lot more (it is SO powerful in our number system), but for now let's just stop and think about what we have just learned.

New Questions to ponder... and then COMMENT on:

• Can you think of a reason why zero is so important and/or powerful?
• Did you ever think of zero as a weird idea? If so, why?
• Can we do all of addition and subtraction with whole numbers now? (I guess I am asking if you think the set of whole numbers is CLOSED under addition and subtraction.) Why/why not?
• What do you think about using zero in multiplication and division problems?

The Counting Numbers... Naturally

The first numbers you ever began to discover were those that came naturally to you, the ones that allowed to realize that there were different amounts, or quantities, of things in the world. As your mind started to see these patterns emerge, someone in your life, probably a parent started to teach you about counting. If you were lucky, you were even taught how to do this in different languages. As you put together the patterns in your head that came naturally to you, with the numbers your loved ones taught you were used for counting, you probably became a counting monster!

I always find it fun to be around a child that just learned to count!

During this time you can learn about a lot of numbers and one fun activity is to see how high you can go, but (here's the really cool part) there is no end! You can go higher forever!

These numbers that you first learn as a child and then continue to use for the rest of your life have a name. They are called (this is a really great name if you ask me) the COUNTING NUMBERS. They are also known as the NATURAL NUMBERS. Both of these names make perfect sense to me because they are the numbers that we kind of already know naturally, but they are also the numbers we use for counting. So what numbers are they, exactly?


A Daze-y Definition

The set of Counting Numbers, or Natural Numbers, includes all of the non-decimal numbers (known as whole numbers - we'll get to that in a later post) greater than zero.  See the symbol and set below:

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11...}

 It is very important to note that ZERO is NOT A COUNTING NUMBER. Zero is a very complicated number (even though it is all about nothing!), so it is something we will address in a later post. Just remember that the counting numbers begin with one and go up from there.

Questions to ponder... and then COMMENT on:

• What's the highest counting number you know?
• How many languages do you know the counting numbers in?
• What things can we do in life with counting numbers?
• What things in life need MORE numbers than just the counting numbers? (That seems crazy... I'm pretty sure I said these numbers would go on forever!)
• Do you remember who first taught you your counting numbers? (Have you thanked them yet???)
• Are you currently being tortured by a counting monster (aka - a child who just learned to count and, therefore must count EVERYTHING in sight)? 

Art created using the Drawing Online website.