Number System: Zero

Zero

Zero shows that there is no amount.

Example: 6 - 6 = 0 (the difference between six and six is zero)

It is also used as a "placeholder" so that you can write a numeral properly.

Example: 502 (five hundred and two) could be mistaken for 52 (fifty two) without the zero in the tens place.

Zero is a very special number ...

It is halfway between -1 and 1 on the Number Line:

Zero is neither negative nor positive, but it is an even number!

The Idea

The idea of zero, though natural to us now, was not natural to early humans ... if there is nothing to count, how can you count it?

Example: you can count dogs, but you can't count an empty space:

Two Dogs		Zero Dogs? Zero Cats?

An empty patch of grass is just an empty patch of grass!

Zero as a Placeholder

But about 3,000 years ago, when people started writing bigger numbers like "42" they had a problem: how to tell the difference between "4" and "40". Without the zero they look the same!
So zero is now used as a "placeholder": it shows "there is no number at this place"

502	Which means 5 hundreds, no tens, and 2 units

The Value of Zero

Then people started thinking of zero as an actual number.

Example:

"I had 3 oranges, then I ate the 3 oranges, now I have zero oranges...!"

Additive Identity

And zero has a special property: when you add it to a number you get that number back, unchanged

Example:

7 + 0 = 7

Adding 0 to 7 gives the answer 7
Also 0 + 7 = 7

This makes it the Additive Identity, which is just a special way of saying "add 0 and you get the identical number you started with".

Special Properties

Here are some of zero's properties:

Property	Example
a + 0 = a	4 + 0 = 4
a − 0 = a	4 − 0 = 4
a × 0 = 0	6 × 0 = 0
0 / a = 0	0/3 = 0
a / 0 = undefined (dividing by zero is undefined)	7/0 = undefined
0a = 0 (a is positive)	04 = 0
00 = indeterminate	00 = indeterminate
0a = undefined (a is negative)	0-2 = undefined
0! = 1 ("!" is the factorial function)	0! = 1

Posted in: Number System, Zero