In integral, would it make any sense to write dx as denominator?

Asked Jul 23 '15 at 10:48

Active Jul 23 '15 at 19:29

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Does it make any sense to write something like this?

$$ \int \frac 1{dx} $$

I think I saw it somewhere, but since I can not find anything similar on wikipedia and wolfram, I have to assume that this is actually nonsese. So is it?

Closest thing found was $ \int f(x) d \alpha(x) $,
but it is not the same as $ \int f(x) \alpha(dx) $.

asked Jul 23 '15 at 10:48

industryworker3595112

May be you can interpret it as $\int \frac{dy}{dx} dy$. If this is independent from $y$. – Zardo Jul 23 '15 at 10:50
Perhaps you saw $$\int \frac{\mathrm{d}x}{x}$$ instead? – Zain Patel Jul 23 '15 at 10:51
2

Maybe $\frac{1}{\mathrm{d}x}=\infty$. – Eclipse Sun Jul 23 '15 at 10:52
After some thought (and deleting my previous comment) I think @Eclipse Sun is right. As the $dx$ gets really small, $\frac{1}{dx}$ goes off to infinity. So you get an infinite sum of terms, each infinite. So I don't think there's much use there. – Colm Bhandal Jul 23 '15 at 10:54
It represent a hipernatural infinite number. In any case it seems that integral diverge or is not defined. – Masacroso Jul 23 '15 at 11:36
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Old joke about this expression: http://math.stackexchange.com/a/304557/7933 – Thomas Andrews Jul 23 '15 at 11:40
@EclipseSun what if the numerator is not 1? – MichaelChirico Jul 23 '15 at 12:16
So I understand now that it is meaningless. Thanks. – industryworker3595112 Jul 23 '15 at 13:09

In integral, would it make any sense to write dx as denominator?

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