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Created assignment and operation.
Added a linkfrom The Continuum Hypothesis to operation.
Actually, in the language that I use, “operation” usually has a different connotation from “assignment”. I almost always use “operation” in the context of algebraic theories and their semantics. The word “assignment” to me is pretty much a synonym for “function” (possibly a class function).
I am curious why you felt a need to write those stubs? To me they read as a bit cryptic (e.g., I don’t know what you have in mind where you write, “sometimes not what one means to say”), and as if you have some unexpressed criticism in mind.
I would probably redirect operation to something like algebraic theory, and I’m not sure what the purpose of assignment would be.
Peter hasn’t answered my question to him in #3, but I can make the following guess: he is referring to the fact that people may use the word assignment informally, in a phrase like “a functor consists of a pair of assignments, one from to and the other from to , such that…” in situations where they would rather not bother formally justifying usage of the more formal-sounding word “function”. For example, see this MO question and the answers given by Ricky Demer and Andrej Bauer, where the OP was unsure of the formal details of class assignment within a framework like ZFC.
I agree with Mike that redirects are generally better than synonym pages – maybe there should be more about this point on one of the nLab usage pages. But if one wants to point out behaviors of mathematicians based on their language use, and what one thinks the underlying unexpressed anxieties might be, I think one should do so forthrightly in remarks on the appropriate pages, and offer technical solutions where possible. With this in mind, I added a technical remark to ordered pair, with a view of solving the little exercise posed by Andrej in his answer at MO. More could be added to e.g. function, specifically the section on class functions, on such (I would say hair-splitting) matters of material set theory, although it’s something we tend not to sweat over – such technical tricks can always be found.
So do you think we should keep assignment?
I’m divided. I think I’d personally prefer to merge to function, but then add more material there on formal vs. informal usages. Maybe we should vote?
If we were to keep it, I’d certainly want it to be less cryptic/more forthright, perhaps along the lines of my previous comment if my guess was more or less right.
@Todd_Trimble: #3 wasn’t answered since I did not know an answer, not knowing to verbalize why it was decided to write it. It is imaginable, though, that people working with the category theoretic literature every now and then decide to look up these terms (even though we all know that everyone knows that such words are not precisely defined) and then find it useful to see the entry and think “aha, in category theory, too, these are useful undefined intuitive nouns, free to use without conflict”, finding confirmed what they were supposing all along. I edited the entries a bit, to make them more forthright.
even though we all know that everyone knows that such words are not precisely defined
I’m not sure we’re communicating effectively here. As I said earlier, assignment to me would be pretty much synonymous with “function” (not “operation”, which for me has a more specific connotation, and I would agree with Mike #4 here). Although I personally am far more likely to use the verb form “assign” (as in “the function which assigns to each element the element defined by…”) than the word “assignment”.
Even if “assignment/assign” are used in informal mathematical speech, I maintain (contrary to the quote above) that “assignment” certainly can be given a precise meaning, and that it should redirect to function, especially to the part on class functions. How one treats the notion of class function depends a bit on which formal framework one is using; e.g., in ZFC proper, classes are not formal objects of the language but are treated as synonymous with formulas in the language (thus, meta-objects), whereas in something like Morse-Kelley set theory, they are formal objects. But anyway, one can make this stuff axiomatically precise.
I still have no idea what the bullet “sometimes not what one means to say” is supposed to convey (that’s what I meant by “cryptic”). Overall, the article as it stands still looks really vague, including the recent addition. At this point I would strongly recommend a merge into function, and we can add more precise material there, including remarks on language use.
I have reworded assignment.
I would vote to merge into function.
I wouldn’t object.
I performed a merge of assignment into function. I did not merge operation into another page; instead I tried to reword it to take into account some of the discussion above, while trying also to retain the gist of what had been there before.
Added one more useful synonym, namely assignation, apparently used much more than assignment (for example in the abstract of R. Garner’s recent “The Isbell monad”, into one section of function and modified that section’s title.
It took me a while to discover why the text was munged (e.g., the math and italicization weren’t rendering correctly) – it was the leftquote ‘ (which I typed by hitting the key to the left of numeral 1). Probably that should be avoided.
Generally the single quote mark (to the right of the semicolon key) works fine. Sometimes a leftquote mark may can be produced where one wants an apostrophe, but that can be fixed by typing a backslash followed by the single quote.
Edit: I should have called the thing in the first paragraph a “backtick”, not a “leftquote”; it’s a special command. Some explanation here.
Thanks for the detailed explanation. Neither the word “munge” nor that the text was in a state giving occasion to using that word were consciously known to me. No incorrect rendering was visible to me.
(The verb “mung” – that’s how I spell it; it’s pronounced with a hard g – is slang. You can find a description here, although I was using it with a much weaker sense; roughly speaking, I meant “botched”.)
I always thought it was pronounced “munzh”.
I guess that would be for the spelling “munge”, right? (I won’t actually claim expertise here.)
Yeah. I wouldn’t either, though; I don’t know whether I’ve ever heard anyone say it who ought to know better than I would.
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