Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Every now and then I read about people who wonder whether zero is a number. It never occurred to me to question this, so I checked the Wikipedia page which, when talking about the Rules of Brahmagupta explains

In saying zero divided by zero is zero, Brahmagupta differs from the modern position. Mathematicians normally do not assign a value to this, whereas computers and calculators sometimes assign NaN, which means "not a number."

I did consider whether this difference in position may be the reason why some people state that "Zero is not a number".

share|cite|improve this question
Related: (In the sense that your question may be an answer to it, or vice-versa)… – ShreevatsaR Nov 16 '12 at 17:15
up vote 7 down vote accepted

A few distinctions:

In your first link, the discussion is regarding whether $0$ is a natural number, not that it is/isn't a number.

Your second link is predicated upon fairly weak, insubstantial first-year undergraduate arguments that can be dispelled with a more rigorous construction of numbers. I also question any blog that concludes a logical argument with "what's your opinion?" (I'd also question the veracity of a mathematical argument coming from a theological blog -- in the same way that I would question the veracity of a monetary policy argument coming from a sports blog).

Finally, the $0/0 = 0$ argument is considered non-standard. That most mathematicians define $0/0 = \text{NaN}$ is not the same as $0 = \text{NaN}$ because these are competing definitions.

So, in short, people often claim "zero is not a number" because they lack the background to understand the formal, rigorous definitions of the number system.

share|cite|improve this answer
Strictly speaking "NaN" is distinct from "is not defined". NaN comes from the specification for floating point values, which computers generally use as an approximation of the real numbers. NaN is a well defined value (actually several, as there are distinct flavors of NaN) with specific properties (such as being unequal to all floating point values, including itself). – camccann Nov 16 '12 at 18:13
Yeah, I was a little loose on my terminology there, overloading NaN with both a computer science definition and an unrelated "not a defined number" definition. – Emily Nov 16 '12 at 18:15
Yeah, that's part of the distinction I'm trying to make--the expression 0/0 has no defined value, i.e., the division operation is not defined on those arguments in the same way that division by "cucumber" is not defined. There is nothing denoted by 0/0 to be a number or not. – camccann Nov 16 '12 at 18:21
Division by cucumber clearly leads to salad. – Emily Nov 16 '12 at 18:22

protected by Asaf Karagila Nov 9 '14 at 8:16

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged or ask your own question.