TITLE: is $dx$ (at least in integrals) a positive real number?
QUESTION [0 upvotes]: Given the Riemann integral: $\int_a^b f(x)dx$
By definition: $dx = lim \frac{b-a}n$ as $n\rightarrow+\infty$. So, is it $dx$ a real number and a positive one as it seems apparent by defintion?
There seems to be a lot of confusion in literature about what $dx$ really is and none agrees that $dx$ is just a positive real number, but I really don't know why!

REPLY [1 votes]: You can think of the $dx$ symbol as just part of the integral notation. The notation makes it looks like a number, because it takes the place of the actual small positive number $\Delta x$ that appears in each of the finite Riemann sums. But these $\Delta x$ values approach 0 in the limit, so there's no actual positive number that the $dx$ represents.
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