I am totally new to the concepts of forms so sorry if my question is trivial. I came across a statement that ''there are no exact $0$-forms as there is no $-1$ form.
So I revisited the definition of an exact form: A form $\omega\in\Omega^{p}(M)$ is exact if there exists a form $\theta \in\Omega^{p-1}(M)$ such that $\omega=d\theta$
In particular, $p=0$ and the above definition confirms the statement, so the degree of any form is a non-negative integer?
On the other hand in one book I read that ''there are no other exact forms that $0$'' How is this possible?
Thank you for explanation
As we're talking about vector spaces (or modules or vector bundles or whatever) rather than sets, then if it's meaningful to utter the phrase "$-1$ form", then we should be saying that the space of $-1$ forms is the zero vector space, rather than saying it is the empty set. In particular, it does have a vector: the zero vector.