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Is there a single word to explain the fraction 0/0?

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closed as too localized by Rasmus, Ilya, Hans Lundmark, mixedmath, Zev Chonoles Nov 1 '11 at 16:07

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..... undefined ..... –  Ilya Nov 1 '11 at 14:43
en.wikipedia.org/wiki/… –  pedja Nov 1 '11 at 14:48
There are two separate words we might use, depending on the context. In pre-calculus we might say this is "undefined." That is, we do not ascribe any value to this. In calculus, we might also call this "indeterminate." They mean slightly different things, because there are forms which are defined but indeterminate, like $0^0$, which we define to be $1$, and there are forms which are undefined but not indeterminate, like $1/0$. –  Thomas Andrews Nov 1 '11 at 14:51
Three words: en.wikipedia.org/wiki/NaN –  Unreasonable Sin Nov 1 '11 at 15:06
One of my calculators is a little cryptic, it just responds with an E. The other is more forthright, and responds with "Error 2," leaving me to wonder what Error 1 might be. –  André Nicolas Nov 1 '11 at 15:54

3 Answers 3

Divison by zero is allowed in so-called Wheels:



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The Wikipedia article on wheel theory could use some concrete examples. –  Michael Hardy Nov 1 '11 at 20:32

Indeterminate .................

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That $0/0$ is "indeterminate" does not mean simply that it's undefined.

$5/0$ is undefined, but $5/0$ is not indeterminate.

That $0/0$ is indeterminate means that if the numerator and denominator both approach $0$, then the fraction could approach anything---either $-\infty$ or $+\infty$ or a finite number, depending on what functions are in the numerator and the denominator. For example, $$ \lim_{x\to4}\frac{x^2-x-12}{x-4} = 7, $$ but that does not mean that $0/0=7$.

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Your first sentence seems to imply that "indeterminate" implies "undefined". According to Thomas Andrews comment above, this is not the case. –  Rasmus Nov 1 '11 at 15:18
@Rasmus Nonetheless the question is about this expression. –  Michael Hardy Nov 1 '11 at 15:30
I don't understand your objection to my comment. Didn't downvote, by the way. –  Rasmus Nov 1 '11 at 15:34
The expression $\frac{0}{0}$ is used, unfortunately, as a descriptor of a certain class of limit problems. But the visually indistinguishable fraction $\frac{0}{0}$ is nonsensical. –  André Nicolas Nov 1 '11 at 15:59

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