## division by zero

In most cases division be zero ends up with not defined , but why do people sometimes call it infinity ?

 Quote by sambarbarian In most cases division be zero ends up with not defined , but why do people sometimes call it infinity ?
Maybe they are being loose. It seems like a bad idea to me.
 You should probably read the FAQs. Your question is bad. In most cases? What does that mean. Look. Dividing by 0 is not defined in the Real numbers. PERIOD. People who call it infinity are either, 1) Don't know what they are talking about and are wrong. -or- 2) Doing very high level math, using a different number system.

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## division by zero

 Quote by Diffy You should probably read the FAQs. Your question is bad. In most cases? What does that mean. Look. Dividing by 0 is not defined in the Real numbers. PERIOD. People who call it infinity are either, 1) Don't know what they are talking about and are wrong. -or- 2) Doing very high level math, using a different number system.
Or 3), they are being loose with terminology and mean it in a limit sense, e.g., ##\lim_{x \rightarrow 0^+} 1/x = \infty##

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 Quote by sambarbarian In most cases division be zero ends up with not defined , but why do people sometimes call it infinity ?
Infinity is not a defined number within the reals..

 Quote by Mute Or 3), they are being loose with terminology and mean it in a limit sense, e.g., ##\lim_{x \rightarrow 0^+} 1/x = \infty##
i think that's it

 Quote by sambarbarian In most cases division be zero ends up with not defined , but why do people sometimes call it infinity ?

"In most cases"? Division by zero is not defined. Period. Certainly some people use to write things like
$$\lim_{n\to\infty}\frac{1}{n}=\frac{1}{\infty}=0$$
but this is either a huge mistake (if the writer isn't aware of what he's doing) or else just an agreed shortwriting.

DonAntonio
 Why doesn't someone just define it!!! ;)

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 Quote by jtart2 Why doesn't someone just define it!!! ;)
Because your definition has to be consistent with your other definitions, and there's no definition you can pick to make it consistent, at least in the usual number systems we work with.

 Why doesn't someone just define it!!! ;)
Before you can define division by zero you have to define division.

Can you do this?

However the question of why is the subject not properly treated in maths classes when they reach a level to appreciate the answer is moot.
 In math it's not defined, but in physics division by zero is infinity. And it's not that physicists don't know what they're talking about, it's just that limits make for incredibly useful approximations, which you need to apply in order to get things done within the human lifespan.

 Quote by dipole In math it's not defined, but in physics division by zero is infinity. And it's not that physicists don't know what they're talking about, it's just that limits make for incredibly useful approximations, which you need to apply in order to get things done within the human lifespan.
This isn't really an issue of limits.The limit of 1/x as x tends towards zero is not the same thing as 1/0. It is a fundamental property of the reals that zero does not have a multiplicative inverse; you can't add one without altering the behaviour of the entire system.

 Quote by Number Nine This isn't really an issue of limits.The limit of 1/x as x tends towards zero is not the same thing as 1/0. It is a fundamental property of the reals that zero does not have a multiplicative inverse; you can't add one without altering the behaviour of the entire system.
That's not really my point, my point was that using the approximation 1/0 = ∞ leads to observable predictions which agree with experiment, so even if mathematically it is incorrect, in physics and other sciences it's enormously useful to define 1/0 to be infinity.

(And one can argue about what's more important, mathematical soundness or physical observation, but at the end of the day planes still fly and bridges don't fall down).
 Physical things deal with quantities that are measureable: you can't measure infinity or make sense of it in a tangible/physical sense so in terms of observation or physical quantification of some kind (for things like science and engineering), it's not useful in that regard.

 Quote by dipole In math it's not defined, but in physics division by zero is infinity. And it's not that physicists don't know what they're talking about, it's just that limits make for incredibly useful approximations, which you need to apply in order to get things done within the human lifespan.

I myself studied some physics while at undergraduate school, and all my best friends were physicists: division by zero is not defined

as infinity in physics, and that's a fact that can be pretty easily checked in any decent physics textbook (in mechanics, optics or whatever).

Now, some physicists can write $\frac{1}{0}=\infty\,$ , just as they can write $\,\frac{dy}{dx}=dy\cdot\frac{1}{dx}\,$ or

absurdities like these: it still is wrong, both within mathematics and within physics, unless there exists an a priori

agreement on what some weird notation may mean, just as writing "s.t." means nothing to anyone not knowing this is usually

taken to means "such that" in mathematics (and perhaps in some other areas as well)

DonAntonio

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