Why is zero a number?

Because it represents the absence of an amount, without demonstrating a negative.

It is mathematical sea level, and critical to an understanding of quantity.

I think there might be two types of answers you’ll get to this (at least).

1) A strict definition of number, which will include zero because it occupies the space between two other integers. Much like all the decimals exist because they represent space between integers, right? Zero would be at least as necessary as 4.698417, right?

2) Zero as a concept. It’s a number because it is a concept that comes up frequently and needs a convenient and concise way to express it. Zero means slightly different things in math and other fields than “nothing” or “null” or most of the other ways to represent similar concepts. We need a word for it like we need a word for “mountain” or “water”...

Why are 2 and 3 numbers? Have you ever seen them by themselves? What about negative and complex numbers? Numbers are an abstraction. They are a convenience and, for reasons that nobody knows, match up nicely with things in the real world. Zero was discovered (invented?) by mathematicians in northern India. They also devised the decimal number system and worked with negative numbers.

@Seek It is mathematical sea level…. Brilliant analogy!

Without it you couldn’t do less than 1 numbers like 0.1234 or .003.

It does indeed represent an amount.

I have four grapes in my hand. I open my hand and give them to you. How many are left in my hand? That’s the amount that zero represents.

According to Amir D. Aczel, author of Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers, the oldest known inscription of the numeral and concept of zero is in Old Khmer (Cambodian) and dates from about 683 AD.

Zero is indispensable to our base-10 system of numbers because it allows numbers to have positional value. We take this system for granted, but remember, the Romans didn’t have it (hence Roman numerals). All computations that depend on place value (ones, tens, hundreds, etc.), even if not in base 10, require a zero as place-holder in order to work.

Zeros to the left basically have no value, but zeros to the right certainly mean something.

Plus, I agree with @Jeruba—zero is a quantity.

Nothing is as important as anything. It provides perspective, and provides the same mathematical value as any other numeral.

Unless you’re talking ‘absolute zero,’ that’s a different thread.