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March 16th, 2010, 11:38 AM   #1
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What type of number is dx?

For example 4 and 2 are natural numbers, -1/4 is a rational and pi is a real.. but my question is what is dx?
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March 16th, 2010, 11:42 AM   #2
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Re: What type of number is dx?

I should have put this in the real analysis one...
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March 16th, 2010, 01:42 PM   #3
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Re: What type of number is dx?

dx is a differential.
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March 16th, 2010, 04:36 PM   #4
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Re: What type of number is dx?

This is somehow merely a notational problem. There is also the problem of identifying a variable in general - what sort of number is y? Well, maybe it's complex, maybe it's real, or maybe not. In general, it's whatever we define it to be, and so it serves as a bit of notation.

What do we take dx to mean? We take it to mean an infinitesimal change in x. To be really precise, different mathematicians use dx differently. The so-called Leibniz notation is different from what I have formally learnt, and he lets dx stand alone as a differential.

What do you think?
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March 16th, 2010, 04:55 PM   #5
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Re: What type of number is dx?

Quote:
Originally Posted by jason.spade
To be really precise, different mathematicians use dx differently. The so-called Leibniz notation is different from what I have formally learnt, and he lets dx stand alone as a differential.
I would like to know every different dx, no matter how difficult they are!
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March 18th, 2010, 11:16 AM   #6
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Re: What type of number is dx?

Well, we're really just getting to different ways of notating differentiation.I can think of four relatively distinct notations.

Leibniz used the prototypical .

Newton used x with a dot over it (I don't know how to do that in Latex).

Lagrange used and so on.

Euler used

And this all becomes a bit more complicated in multivariable, so I'll just say that you should be familiar with many before you try multivariable. I used to dislike Leibniz notation for multivariable, but it is very accepted and I have since gotten used to it.
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March 18th, 2010, 01:18 PM   #7
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Re: What type of number is dx?

dx by itself is used to denote the variable of integration, under an integral sign.
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