I saw a YouTube video that messed up all my intuition. They were calculating the integral of something like -1+x^dx which in the end he solved by taking the limit as dx->0 and he got the solution. But everyone in the comments was saying complex stuff like like “well to be rigorous x^dx can be thought of an element of C*(R,R), the exterior algebra on R”. Huh. When did dx get any different from lim x->0.
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It’s just terminology basically. The abbreviation “dx” just stands for “Delta x”, where “delta” refers to a change. So, delta x, or dx, just refers to the change in the “x” coordinate.
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