Nevertheless, having multiple misspellings in every sentence makes a bad impression. For example, people are more likely to answer questions that are well-edited, etc. Your writing is the only window we have into you as a person, after all.
Right, that works. I'm wondering if there's a way to see it without appealing to the diagonalization, though. (Because if you're going to diagonalize, why not just do that in the first place and be more explicit?)
I see what you're trying to do, but is this enough? All you've shown is that the spectrum of the limit is just $1$, which I don't think uniquely characterizes the identity. Or does it?