In a document it said module aims and under that in the paragraph it said "the chief objective of this module...". One person said it's wrong to use two different words like that. The other said they both mean the same thing.
@XanderHenderson yeah. That's what I thought too. But the person who said aims and objectives are different said even the word chief should be changed to primary
If you are just trying to write in plain English, then "objective", "aim", "goal", etc all mean about the same thing. It is good writing style to avoid using the same word over and over again, so it is good writing to use several different words in one passage.
@RyderisnotRude. No, I disagree. The "chief objective" is the main or primary objective. It needn't be "made of many objectives". It is simply the most important objective (in plain English).
(At least, not in vernacular English. In a technical document, in education, "objective" typically has a specific meaning in American education, i.e. an "objective" is a testable, measurable bit of knowledge or ability that students are expected to be able to desmonstrate).
@BuddhiniAngelika Like I said, the plain English, the words have little distinction. But in an educational setting, they can have technical meaning, as prescribed by accreditation agencies, institutional standards, etc.
If you are writing for an audience which will be familiar with that technical distinction (or for whom that technical distinction matters), you need to make sure that you are familiar with the vocabulary that they use.
For example, at my institution, "objective" has the specific meaning I've given above, while "aim" would not be used in our curriculum documentation.
@BuddhiniAngelika Well, if it is given to leadership, I suggest that you talk to your leaders about what they believe the words mean, and how they expect them to be used. Random strangers on the internet cannot help you.
What's the best choice to do: if the institution chief who doesn't have a background in mathematics says "okay this should be aims but not objectives", even if others with mathematics knowledge says they both mean the same, even if we feel maybe the chief might be just putting on a bit show of her power, we would have to just agree with her right?
Like I said above, "aim" and "objective" are not mathematical jargon, they are educational jargon (if they are jargon at all). If your boss says "it should be 'aims', not 'objectives', then FFS, write "aims". This has nothing to do with mathematics.
She gives me the impression that she's just making a bit of a biased statement, and criticising on purpose, maybe because she doesn't have a PhD but only a Masters but the person who originally wrote this has a PhD
It doesn't matter what other people with a background in mathematics feel. This isn't a mathematical question, and their opinions are irrelevant if your boss is telling you to use a particular term.
@BuddhiniAngelika I would suggest that this is not a healthy attitude for you to have.
@XanderHenderson a lot of that 'educators' could probably also be 'educators recently educated in north america,' i wouldn't assume any of this jargon travels well
like in the UK maybe they're Quests and in AU they're Toffy-Woffies
(At least, not in vernacular English. In a technical document, in education, "objective" typically has a specific meaning in American education, i.e. an "objective" is a testable, measurable bit of knowledge or ability that students are expected to be able to desmonstrate).
I've observed that some people do more significant mistakes, like teaching some mathematics concepts wrong etc., sloppy documentation with equations typed incorrectly. But they talk a lot like in a very sociable way and it seemed that their mistakes however are not being commented by her. So maybe that's why I might have felt there's a biasedness. I felt like maybe for people who don't put on a good talk this happens
xander: the difference between aims and objectives is i aim the list of objectives at the wastebasket. i don't have time to teach, let alone test, euler's method in calc 2
From what I've seen you say, you seem to have a bias against people who aren't as highly credentialed as a person with a PhD. But I see no evidence that your boss has any such bias.
Buddhini AngelikaBuddhini Angelika 3:14 I've observed that some people do more significant mistakes, like teaching some mathematics concepts wrong etc., sloppy documentation with equations typed incorrectly. But they talk a lot like in a very sociable way and it seemed that their mistakes however are not being commented by her. So maybe that's why I might have felt there's a biasedness. I felt like maybe for people who don't put on a good talk this happens
You are the one who suggested that your boss is biased because they do not have a PhD. In general, when someone says something like that to me, I tend to reflexively believe that the person saying that is expressing a bias against people without PhDs.
I mean for mistakes like above nothing had been done. But she started to exert a lot over this document. That's what I meant...
@XanderHenderson okay
@XanderHenderson Yeah. Some others have openly expressed their jealousy regarding the few people with PhD. Maybe because of that I felt maybe the boss is also the same. I just mean "maybe"
@Jakobian yeah :) can you pls tell me if it's not a trouble?
@Jakobian still meditating on this :) Is it not good to write $\int f < \infty$ when speaking about integrability? I guess your point is that $\int f$ could be ill-defined, oscillate or whatever, but I can't think of a concrete example.
@XanderHenderson I don't have any bias regarding either party.
I'm just introverted. Not good at doing a lot of social talk. I didn't observe that type of talking from the person with the PhD who designed the outline earlier either though. I'm just bit worried that I might not be talking enough
Or I might not be able to balance out the social things, or internal politics, in the office environment due to my introverted nature
@BuddhiniAngelika Everyone is biased. You should examine your biases in this case. To me, an outsider, it sounds an awful lot like you are engaging in credentialism, i.e. devaluing the work and contributions of others because they don't have advanced credentials.
If you are just trying to write in plain English, then "objective", "aim", "goal", etc all mean about the same thing. It is good writing style to avoid using the same word over and over again, so it is good writing to use several different words in one passage.
@BuddhiniAngelika I don't know what your intention is. I am telling you what I, as an uninvolved third party, am seeing. I am trying to describe to you how you come across to me.
I just mentioned the situation with others around me and just mentioned my worry regarding my introverted nature, hoping that if there's any suggestions for me to overcome it you'll tell that too
I honestly don't care if you are "like that" or not---I don't know you, and I don't interact with you that much. But when someone says "Hey, you are being a little [x]," it is generally best not to get defensive and say "No, I'm not!" You don't have to respond, or you can say "Oh, I'll think about that". For better or worse, getting defensive kind of confirms people's judgements.
Fair point @Xander. OTOH, it may be confusing to use a bunch of different words, just for the sake of variety, if it leads to situations like this discussion on aims / gials / objectives. Especially if the primary readers of the document are ESL speakers, and the authors are also ESL speakers.
@PM2Ring My advice was for an audience consisting primarily of native English speakers, with an expectation that they were at least literate to a college level. If you are writing for a younger, or non-native, audience, you definitely want to cut down on vocabulary.
@Jakobian I have to ask...what's gross about writing $\int f<\infty$ for $f$ real-valued, assuming $f$ satisfies the definition of $\int f$, i.e. having at least one of $\int f^+$ and $\int f^-$ finite?
I think that by the time one reaches measure theory class, the (affinely) extended real line should have been introduced. If so, then $+\infty$ is an actual value that you can manipulate, and not just syntactic sugar for some statement about convergence. $\int f<\infty$ would then mean, literally, that the integral of $f$ on $(-\infty,\infty)$ exists and is less than $+\infty$, i.e. it is an affinely extended real number that is not $\infty$.
Either way I wouldn't try to begin on writing $\int f$ if I didn't know that I can define what $\int f$ is. That's why for non-negative functions it makes sense, but for functions which aren't non-negative one would have to say the integral of $f$ in extended sense exists. I don't agree at all with $\int f < \infty$ as a substitute for existence of $\int f$
@SineoftheTime No, I don't know anything about differential forms. It is a result in distribution theory. The derivative passes from one side of the dual pairing to the other---I just don't remember the details.
I just mean that it should be interpeted as an inequality between extended real numbers, not as some special statement where $\infty$ is just a shorthand for something else...
Oh, I think what I wrote was misunderstood. I just mean that saying "$\int f$ exists" has a different meaning to "$\int f <\infty$". What I think the latter statement means is what Xander wrote.
So the statement $\lim_{x \to a} f(x) < M$ means (a) that $\lim_{x \to a} f(x)$ exists and (b) the value of that limit is smaller than some bound $M$.
The statement $\lim_{n\to\infty} (-1)^n < 2$ is meaningless, since the expression on the left is meaningless / doesn't exist / however you want to describe that non-limit.
@XanderHenderson hmm, it's unclear to me if $\int f<\infty$ also means that $\int f\neq -\infty$ for instance. After all, $-\infty<\infty$. Maybe this is becoming meta-mathematical, if that's the right term for it.
@Jakobian You seem to be implying that mathematical writing is context independent. If you have somewhere assigned a meaning to that limit, and you are in a context in which that notation has meaning, then the statement "the non-limit $\lim_{n\to\infty} (-1)^n$ has no meaning" is no longer true, and the inequality is fine.
What you would be saying by writing $\lim_{n\to\infty} (-1)^n < 2$ in that context is (1) the limit on the left meaningfully exists (in the context in which I am writing), and (b) that limit is less than 2.
But I think that your biggest hurdle is that if you want to give meaning to $\lim_{n\to\infty}(-1)^n$, most mathematicians would add some decoration to the notation to indicate that this is not the "usual" meaning of the llimit.
@psie If you are working on the extended real line, then it is, in fact, true that $-\infty < \infty$. And $\int f = -\infty$ is a meaningful value of that integral---it can reasonably be said in that context that $\int f$ has meaning (the integral does not converge, but it has the value $-\infty$.
But I was thinking more in the context of nonnegative functions---I can modify my previous statement to "(b) either $\int f$ is finite, or $\int f = -\infty$."
