There's, oh, one word in there that doesn't mean exactly what it does in vernacular (agent- someone capable of acting)- I hate philosophers who construct their own languagespaces.
Yes. However, there is a certain surfeit of commas I find most intrusive.
I'm also going to agree on the languagespaces thing--it's like those idiots who think they can invent their own notation for everything. Vargh.
Use it in your personal notes, but make your damned textbooks comprehensible!Principles of Mathematical Analysis[/i]]Let f: X -> Y be a continuous function, X a compact metric space, Y a metric space. Then f is uniformly continuous.
In this example, though I understand the concept of a continuous function(lim(f(x), x->x0) = f(x0) ∀ x0 ∈ range(f))...this definition makes no sense to me, prima facie, because "compact" "metric" "space" all are jargon terms that I, as yet, do not know.
Ah, but it's more of a comment on style than anything else. Who cares what the words are? You know which pieces of the puzzle you're working with. Everything is right there in your hand: conditions, concepts, the beginning, the end. There is no need to go digging for
what, precisely, Rudin means by this or that. "Now, I know he's talking about a compact metric space, but what does he
mean by a compact metric space in this instance? Why are there all these qualifiers in front of the metric space? Why is he mentioning this fact, or another? Why use this word density when addressing that particular notion? Does it mean that notion is more important, or did he just forget to word-prune again?"
I should probably restate that a bit. What I mean is that even though you may not know the precise meaning of the jargon, you know exactly what you
don't know, and you know exactly what you
do know. You can also recognize that, once you understand those three words, the entire phrase will make perfect sense to you with no digging.
Consider instead this reformulation:
If f is a continuous function, though not necessarily bijective, injective, or surjective--i.e., a relation with certain key properties--from a compact metric space X with metric dX to a metric space Y with metric dY, then we have that f is uniformly continuous over X into Y.
We no longer know what is meant by a function, even. Someone has introduced all these extraneous notions--bijectivity, surjectivity, injectivity--and we must recall their definitions, as well. Further, there is this nonsense about a function being a relation. No, a function is a function. There's no need to remember that it's a relation, too. Why stick in extra information where you don't need it? The terminology is precise enough without saying that all this extraneous crap
might be possible in the classification of f.
Attempts to be precise frequently result in more mental fuzziness on the part of the reader. Unneeded specifications and qualifications tend to detract from clarity, rather than add to it.
The paucity of qualifiers and punctuation puts a greater emphasis on the concepts themselves and their comprehension, not on any attempts required to exhume a thesis from musty rhetoric.
That's some good musty rhetoric! 
I know
It's my curse--I'm generally good at old-fashioned formal writing, but I have trouble reading it. My professors seem to like it, though >_>
As far as my fiction writing goes, I hear it's vaguely Faulknerish (previously they said Joyce, after which I decided I had to clean up my act a little). Makes me wonder how incomprehensible I really am.
Darn it, now I'm getting a hankering for an English class.
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