The Number 0

Background 

We've covered Counting/Natural Numbers, which is the number 1 and then the next number is plus 1, so 1, 2, 3, 4, ...

Question 

What about 0? 

Answer 

Zero took a long time to come into its own as a number. See below for a very brief history.

Analysis 

While it's pretty straightforward to recognize the existence of a thing and then count it (like with the number 1), the concept of 0 took a lot longer to come into existence. And it makes sense - how do you count absence? Non-existence? Nothing?

Consider a situation where you have 2 eggs. You then make an omelette with those 2 eggs. You had 2 eggs and now you have... well... no eggs!

The history of the Counting/Natural Numbers is lost in the mists of time across a whole host of cultures, the same can't be said for 0. For many civilizations, there was no need for 0. The Romans, for instance, had no symbol for 0 at all - the way they wrote numbers didn't require placeholders. For instance:

I = 1

II = 2

III = 3

IV = 4

V = 5

VI = 6

VII = 7

VIII = 8

IX = 9 

X = 10

and the symbols continue with ones for 50, 100, 500, and so on. No need for zeros. (See the post on Roman numerals for more).

However, if you have a number system such as our current 10 decimal system (known as base 10) where we can make all of our numbers from the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and putting them into different places (1's, 10's, 100's, and so on), where the need for a 0 to hold a place would show up. Before 0, that particular place would simply be blank. And so the numbers 11 and 101 would look like this:

11

1 1

Is that second number really 101? Or is it 11? Perhaps a 1 and another 1?

Even with that, it was only the mathematically advanced civilizations of Sumeria, India, and the Maya who used the number 0. For the Sumerians and the Maya, 0 acted only as a placeholder in larger numbers - it was never a number in and of itself.

But it was 5th century India, where the concept of "emptiness" and "emptying the mind" were coming to the fore and becoming part of religious texts, that a symbol arose to help express that emptiness. If 1 is the number for the Self, then 0 is the number for the empty mind.

Once zero was introduced as a symbol for an actual value, it started being used in mathematics. Questions such as 2 + 0 = ? made sense - and it's this ability to ask that kind of question that leads to algebra (we'll discover that in later entries).

Vocabulary:

• Counting/Natural Numbers - The set of numbers that starts with 1 and increases by 1 (1, 2, 3, 4,...)

For more information check out these links (comment to add a resource to the list!): 

Live Science article on the History of 0
http://www.newworldencyclopedia.org/entry/0_(number)

Where might you have come from? 

Fact-orials Index

Numbers:

• The Number 1
• Counting/Natural Numbers

Operations:

• Addition

Where might we go?

Numbers:

• Whole Numbers
• Prime and Composite Numbers
• Expressing Values, and Bases

Operations:

• Multiplication
• Division

Operations with different kinds of numbers:

• Addition, Subtraction, and Whole Numbers

Algebra