〈 Berger | Dillon 〉

I mean, this is one justification, but certainly doesn’t justify it being a fraction. You need a multiplicative inverse of dx to have a fraction.

Okay so I actually know more about this book/author than I really should. If anyone wants to buy me a kindle copy, then *please* do The only thing I’ll say right now, is that the Wheeler quote on the cover is clearly from a PhD letter of recommendation, and not a book review

I legitimately still don't understand why it can't be a fraction

The notation is misleading. For dy/dx to be a fraction, you need to strictly define what “dy” and “dx” are. Moreover, they have to be things you can divide. You could rigorously define concepts like dx and dy, and then you’d have “1-forms”, but you can’t divide them.