Zero

Zero Number Is zero a number? Two ways to answer this one, the simple answer and the complicated mathematical answer.

The simple answer: Yes, zero is a number but you are not alone if you wonder why. Indian mathematicians first came up with the number idea around 650 AD. Originally, perhaps as early as 200 AD, they used zero as a placeholder in another number. For example, in our notation: 216 is a different number than 2016. This use of zero advanced trade, commerce, and bookkeeping but does not qualify zero as a number. Zero, in its place-keeping function, is a kind of punctuation mark to help us interpret numbers correctly[1].

The mathematical answer: Zero is clearly an element of the set of Real Numbers, it’s the “additive identity” — the number that, when added to any other number x, doesn’t change the value of x. (Similarly, 1 is the multiplicative identity — the number that, when multiplied by any other number x, doesn’t change the value of x.) Thus, zero is a number, just as any other element of the set of Real Numbers is a number.

But before you get to the Real Numbers, you probably start with the Counting Numbers or Natural Numbers, the set N = {1, 2, 3, …} in set notation. Zero isn’t a member of the set of Natural Numbers since you normally don’t start counting with zero. A primitive society developing a counting system wouldn’t think of “none” … they’d start counting with “one.” Thus, if by “number” you mean “the set of all Natural Numbers,” then zero isn’t among them. Of course, the concept of zero makes its appearance pretty early historically (the idea of using zero as a placeholder digit comes later, but that’s notational, and a different story)[2].

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