[lindboe]

With respect to [2] - I think this is partially our garden-variety, universal impostor syndrome, but not only that: even otherwise good papers can be written so poorly as to be nearly incomprehensible, and still get published! I've come across papers that seem to be genuinely valuable and interesting work, but the amount of mental manual labor required on the reader's part is horribly daunting - mishandling or absence of grammatical articles ("a", "the", etc.), inconsistent spelling, a feeling of constant ambiguity of meaning...

I have great sympathy for the many excellent scientists who have to overcome a language barrier to get published, since the lingua franca of virtually every major journal is English. It's not inherently bad that "the language of science is bad English"; these difficulties are a symptom of pulling together good science from everywhere in the world. I'm just deeply irritated with the publishers - IEEE in particular, though the fault is by no means theirs alone - who don't care to keep up a copyediting standard for their allegedly high-quality publications, since apparently their goal is not to communicate science well, but instead to make a profit.

(I distinctly remember one of my favorite math professors stating, in no uncertain terms, that the words "a" and "the" each have different connotations with respect to existence and uniqueness. Incorrect use of either would get points knocked off of your proof.)

[raincom]

The existential quantifier(∃) and the unique existential quantifier (∃!) of Predicate logic correspond to "a" and "the".