Hi, I fixed those mistakes. I hadn't even noticed this one:
> The picture changes, however, if we let the formulas to contain an infinite number of operations.
because I'm getting so used to Germanic English.
I fixed your equation in a different way than you suggested, by deleting $e^1 = \exp(1)$. I think writing $e = e^1 = \exp(1) = X(1)$ is only interesting for the tiny minority of people who are maniacally concerned with formalisms and how different formalism are related (like me). Most people will consider it either confusing, or boringly lengthy throat-clearing.
I can reinsert these extra equations and add an extra line to the equation if you want.