In Riemann Integral, one can intuitively interpret $dx$ as infinitesimal, and it makes sense, but in differential forms, it lost this interpretation, is there a way to make connection between these two?
The $d$ in $dx$ as infinitesimal can roughly be interpreted as a function ($\Delta f \approx f'(x)\Delta x$). So what I'm asking is another direction, namely, Is there a way to interpret ($dx$ as 1-form) as ($dx$ as infinitesimal)?
Based on my very limited knowledge, I think the differential form stuff is an axiomatic system, right? You defined some rules, and you play with it. So you can interpret any way you want, as long as it makes sense, (because it's just symbols).