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

Zero is neither negative nor positive. But it is an even number.

## The Idea

The idea of zero, though natural khổng lồ us now, was not natural to early humans ... If there is nothing to count, how can we count it?

Example: you can count dogs, but you can"t count an empty space:

Two DogsZero 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 people needed to lớn tell the difference between numbers lượt thích 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", lượt thích this:

 502 This means 5 hundreds, no tens, và 2 ones

## The Value of Zero

Then people started thinking of zero as an actual number.

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### Example:

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

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

### Example:

7 + 0 = 7

Also 0 + 7 = 7

This makes it the Additive Identity, which is just a special way of saying "add 0 and we get the identical (same) number we 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

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