# What is "?"

Discussion in 'Off-Topic' started by DMOC, Sep 26, 2009.

1. ### DMOCMathematician

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I have a calculus problem that gives me a really long function of x equation (too long for me to type in a reasonable amount of time ).

And after the long equation, this: &#8712; appears.

x &#8712; [4, -2]

Does this mean that (4,-2) is a point on the graph? I know that the symbol means it's an "element of" but I'm still unsure.

2. ### ZeligBeep Boop

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This is a question you should ask your teacher, that's what he or she is getting paid for.

3. ### Elta我不会把这种

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It means you fail

4. ### Bill3000OOOH NOOOOOOO!Supporter

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Shouldn't you know this already? You're a Mathematician, after all.

5. ### DMOCMathematician

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My teacher didn't tell us. She gives us heaps of stuff without telling us stuff.

6. ### laffyChieftain

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x belongs in a closed interval.

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8. ### DMOCMathematician

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She's refusing to tell me. I wouldn't have started this if I didn't ask her.

Edit, sorry I should have been more clear in my previous post.

9. ### Tee KaySilly furry

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x &#8712;[-2, 4] would mean that the function is defined for the x values between and including -2 and 4 (that is, the domain is [-2,4] ). I've never seen it with the higher value at the front though.

10. ### DMOCMathematician

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So maybe she made some mistake?

Hm ... I'm going to skip that problem.

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It might be helpful if you posted the whole question, for a bit of context...

12. ### nc-1701bombombedum

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I'm a math major, but I've only just reached Calc 2 at this point.

It appears to me that your problem is just stating that your function is a member of the list [4, -2], though depending on the context I think it may be a sequence? I haven't done very much with these types of things yet, but my guess is that it is saying your equation is valid only if x is a member of that list.
Though depending on what calc your doing (1, 2, or 3) it could be significantly more or less complicated. In Calc 1 I did problems that looked similar to that where the [4, -2] was simply saying that these were the endpoints of the closed interval. So you would have to integrate/differentiate based on those endpoints...

Hope some of that helped, feel free to ask for more clarification or expansion on that if it doesn't help. Though if your in Calc 3 I probably won't be able to help you any.

13. ### DMOCMathematician

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nc-1701 I think you got it. Thanks.

I'm in high school now so no calc 1 2 or 3 We have levels AB and BC for the A.P. exams

14. ### RashiminosFool Prophet

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x is an element of the closed interval [4, -2], so -2 <= x <= 4, ...

but usually standard interval notation places the lower value on the left.

So it should be [-2, 4].

This means x is an arbitrary value from the interval, and I would think the problem requires you to state something about each possible value of x in that interval and how it affects the given function.

It's not the point (4, -2), as that's an ordered pair and would be denoted differently:

x,y &#8712;R such that (x,y) &#8712;R^2

15. ### EarthlingDeity

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Yes, both taillesskangaru and Rashiminos have what seems to me really the only possible interpretation - it's simply defining the domain of the function, which is better written as [-2, 4]. And you should do the problem anyway

16. ### RashiminosFool Prophet

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I never said anything about [-2, 4] being the domain. It's not clear from the information presented that the domain is what the interval represents.

Without knowing what sort of problem it is, there are several different reasons for x &#8712;[-2, 4] to be there.

(Defined? Continuous? Differentiable? Maxima? etc...)

17. ### nc-1701bombombedum

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The interval seems most likely, especially given that this is High School Calculus. Now if we know what type of problem they had been doing in class and had the exact problem copied here we could probably be more exact, but as it is I think it probably just represents the interval overwhich you will be differentiating/integrating over. As far as I know there is no strict reason why the smaller number needs to written first, it's just often done that way.

18. ### RashiminosFool Prophet

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It depends on what notation is being used, and lower to higher is fairly common.

I assume we don't have nonsense like 4 <= x <= -2 going on when the reals are an ordered set.

19. ### MaxxieChieftain

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That is a symbol used in set notation. Read it like this:
{x | has a certain property}
where that property could be anything.

Your example means the set of all x such that x is a member or element of the real (?) numbers contained in that interval. Basically, it wants you to find all values of x in that interval that satisfy the long equation you mentioned. You'll probably need to write your answer based on n, where n is any integer or whatever you need for your answer to work.

You must be starting to work more with proofs so you'd do well to review the various propositional logic symbols now too. When working with proofs pay careful attention to every single symbol and double check the meanings if you aren't 100% sure. For example if you see &#8712; with a line through it (mathematica fonts don't work here so just imagine it), that means &#8220;not &#8712;&#8221; or &#8220;not an element,&#8221; of whatever follows.

There is usually more detail about set notation in finite and discrete math books so you should find one to study all of this.

20. ### mrt144Deity

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Sets suck except when you start having to running SQL queries.