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On April 08 2011 11:35 Zeke50100 wrote:Show nested quote +On April 08 2011 11:34 shinosai wrote:On April 08 2011 11:23 StarStruck wrote:On April 08 2011 11:09 shinosai wrote:
Hmm. I got it wrong, but I'm not really bothered by it. My calculus book never had such poor notation. Parenthesis are your friend. I think this thread really just amounts to people being annoyed by bad notation (not necessarily wrong, but bad nonetheless). In the math classes that I took, using parenthesis to make your work clear and concise was mandatory. That's calculus though. When you see a problem written in the following you have to ask yourself. What is this problem asking? There are only 3 things. Brackets, division and multiplication. What does this tell you? One of the first things you learned about operations. What you see is what you get. Poor form or not. Sure, it's poor form to the scholarly eye, but you should have an idea of what they're asking based on the shitty form alone. There's a reason why you don't see ÷ used so much anymore! That's like the first indication. Grade school math. Order of operations! :O The fact you guys are saying it's ambiguous should tell you it's an elementary question asking you to use the order of operations. I didn't say it was ambiguous, but it is bad notation. Now, I know you think this should make me feel bad because this is grade school math. However, it doesn't, because the practical application of bad notation is zero. What I'm trying to say is, bad notation like this is something you will almost never come across. It's like making fun of someone for misinterpreting an English sentence that was written with an odd word order. We come across these all the time, and instead of making fun, why not just clarify by writing in standard word order? I'm never going to have to apply trigonometric identities in real life. Does that mean I should ignore its existence?
Trigonometric identities have useful functions for solving problems. Please detail me on what exactly is useful about bad notation in comparison to standard notation? This is one that I would love to hear.
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AN EXAMPLE OF AN AMBIGUOUS QUESTION:
What is the square-root of 4?
See how that's ambiguous? See how it cannot compare to the OP's poll-question?
On April 08 2011 11:38 shinosai wrote:Show nested quote +On April 08 2011 11:35 Zeke50100 wrote:On April 08 2011 11:34 shinosai wrote:On April 08 2011 11:23 StarStruck wrote:On April 08 2011 11:09 shinosai wrote:
Hmm. I got it wrong, but I'm not really bothered by it. My calculus book never had such poor notation. Parenthesis are your friend. I think this thread really just amounts to people being annoyed by bad notation (not necessarily wrong, but bad nonetheless). In the math classes that I took, using parenthesis to make your work clear and concise was mandatory. That's calculus though. When you see a problem written in the following you have to ask yourself. What is this problem asking? There are only 3 things. Brackets, division and multiplication. What does this tell you? One of the first things you learned about operations. What you see is what you get. Poor form or not. Sure, it's poor form to the scholarly eye, but you should have an idea of what they're asking based on the shitty form alone. There's a reason why you don't see ÷ used so much anymore! That's like the first indication. Grade school math. Order of operations! :O The fact you guys are saying it's ambiguous should tell you it's an elementary question asking you to use the order of operations. I didn't say it was ambiguous, but it is bad notation. Now, I know you think this should make me feel bad because this is grade school math. However, it doesn't, because the practical application of bad notation is zero. What I'm trying to say is, bad notation like this is something you will almost never come across. It's like making fun of someone for misinterpreting an English sentence that was written with an odd word order. We come across these all the time, and instead of making fun, why not just clarify by writing in standard word order? I'm never going to have to apply trigonometric identities in real life. Does that mean I should ignore its existence? Trigonometric identities have useful functions for solving problems. Please detail me on what exactly is useful about bad notation in comparison to standard notation? This is one that I would love to hear.
I never said bad notation was useful. You, however, are saying that you shouldn't need to know bad notation at all, essentially ignoring that it is completely legitimate and legal.
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On April 08 2011 11:07 Zeke50100 wrote:Show nested quote +On April 08 2011 11:06 jtan wrote:
There also seems to be some different use of the word ambigous.
The expression 1/x*y is unambigious in the strict computer-sience sense, but like I said, it's ambigious in the sense that a lot of people interpret it differently, you can't really argue against that. Lack of knowledge does not mean ambiguous.
Problem is when none uses the rule in practice, which from my experience is the case of 1/xy. My math professors used (as seldom as they used one line notation) 1/xy as meaning 1/(xy), even though everyone knew that it is not correct according to the order of operations rule. So if you asked people there what 1/xy means the answer 1/xy = 1/(xy) would be correct as universal usage supersedes not used rule and creates new variant of the notation. I would assume a lot of math communities use it the same way ?
So when OP asks his question and does not specify notation it is in fact ambiguous. You cannot always assume everyone uses the same notation. If you write (48/2)(9+3) you can assume reasonably that everyone's notation interprets it correctly. In case of OP's formulation, that assumption gets much weaker.
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If anything it's a bad math problem. -.-' I don't get why people think that getting 2 is so atrocious. Probably just internet elitism :S. To be perfectly honest, I don't think we're sitting around in universities debating 4th grade mathematics, so I guess I get to puff my pipe and contemplate how childish the people are whose heads get bigger off this thread just because they paid more attention in 4th grade when they didn't know what pot is.
Be careful guys! Being able to multiply at a 4th grade level is great power, and with it comes great responsibility!
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Lol I just think that some math/science people are bugged because it's such a stupid question...
Rules are designed for clarity - abusing the order of operations, which is designed to make expressions unambiguous, to create a trick question is kind of stupid (for the record I immediately got the right answer - why else would such a stupid question even be asked lol)
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On April 08 2011 11:34 jtan wrote:
zeke, space_yes, jalstar and all of you arguing this, how much math did you take?
Just curious...
I am double majoring in applied computational and mathematical sciences (ACMS) and statistics at the University of Washington. I've taken your first year calculus run (differential, integral and multi-variable), vector calculus (different universities have different names for this course, covers Stokes Theorem, divergence, curl etc), ordinary differential equations, partial differential equations, linear algebra, and numerical analysis so far.
I have about two years left. Looking forward to my discrete math classes next fall 
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How on earth did this thread get 44 pages, are people that silly?
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On April 08 2011 11:37 Zeke50100 wrote:Show nested quote +On April 08 2011 11:36 crate wrote:
I sure as hell would never interpret 1/xy as y/x, for what that's worth. I'd always see it as 1/(xy). (Neither would I write it that way; I'd add in parentheses for clarity as in the second sentence.) "Clarity" in this case is completely unnecessary, because 1/xy = y/x is a mathematical fact.
So? (33+3+14)/(6+9+10) = 50 is a mathematical fact, yet writing the former is hardly a good example of clarity.
Uncommented code compiles perfectly but you'd never want to turn it in for a project.
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On April 08 2011 11:37 MadVillain wrote:Show nested quote +On April 08 2011 11:32 Zeke50100 wrote:On April 08 2011 11:29 MadVillain wrote:On April 08 2011 11:25 phantaxx wrote:On April 08 2011 11:16 MadVillain wrote:On April 08 2011 11:13 Zeke50100 wrote:On April 08 2011 11:11 jalstar wrote:On April 08 2011 11:10 Zeke50100 wrote:On April 08 2011 11:08 jalstar wrote:On April 08 2011 11:07 Zeke50100 wrote:
[quote]
Lack of knowledge does not mean ambiguous. Are you really trying to argue that hundreds of people don't know order of operations, or am I missing something? Yes. Hundreds of people (those who have bothered to reply, anyway, which is indicative of response bias in the first place) just don't know their stuff. You can't be serious. I just refuse to believe you're serious. You really can't see how the problem is a trick without assuming complete lack of order of operations knowledge? What the fuck? I never said a complete lack of knowledge. You might want to look up what knowledge means. Somebody's ignorance of the fact that you do not, indeed, multiply 2 by 9+3 before proceeding with the rest of the simplification is a lack of knowledge. But that is not why people got the question wrong. They got it wrong because they assumed that 2(9+3) is being used as a single unit which it often is in a mathematical setting. Nobody was lacking the knowledge of order of operations as you're claiming. Face it, by definition the question is ambiguous. I'll post the definition again in case you missed it: "Ambiguity is a term used in writing and math, and under conditions where information can be understood or interpreted in more than one way..." People "interpreted" the 2(9+3) to be one unit it can also be interpreted as not being one unit. There are two ways to interpret it. Two is more that one. It is ambiguous. Clear? I don't think you have the "knowledge" of what ambiguity is. If I interpret 2+4 * 6 as (2+4) * 6, that doesn't mean it is ambiguous. I would just be wrong. But under no mathematical setting do people ever interpret 2+4*6 to be (2+4) * 6, that is a silly facetious example. Do you actually think that people in a university setting interpret 1/xy as (1/x)*y ? No, they don't. The ambiguity arises from the fact that 2(9+3) is commonly viewed as a single unit, just as xy is. Under no mathematical setting? Guess what? He just did. EDIT: You think universities don't recognize 1/xy as y/x? What university are you talking about? Ok you're clearly being flippant, how can you reasonably say that the general population would view 2+4*6 as (2+4)*6? The second poll in this post CLEARLY shows that people interpret things differently. He just made that example up for sake of his poorley executed argument. The general population, especially in a mathematical setting in a university would NEVER view the statement like that.
I think the polls just prove how people don't think about what they're doing.
Oh, and I think there is no way people could reasonably think the answer to the OP's question is 2. People who do are just being stupid. See how far that gets us?
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I think the 1/xy ?= y/x is a good example of what I was trying to say. To me, 1/x*y is a different looking thing than 1/xy, and I would read them differently.
If the OP had truly intended for the answer to be 288, wouldn't he have written 48 / 2 * (9 + 3)?
So, I say either the answer is 2 and the question was written in a strange way, or it's 288 and designed to point out a grouping/ordering tendency in human nature.
I think a VERY interesting idea would be to pose this question to different ages and education levels, including math specialists, and compare THOSE results.
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On April 08 2011 11:38 Zeke50100 wrote:
AN EXAMPLE OF AN AMBIGUOUS QUESTION:
What is the square-root of 4?
See how that's ambiguous? See how it cannot compare to the OP's poll-question?
Ok, you don't know what ambiguous means. Hint: it doesn't mean "multi-valued".
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On April 08 2011 11:33 ghrur wrote:Show nested quote +On April 08 2011 11:25 MadVillain wrote:On April 08 2011 11:17 Zeke50100 wrote:On April 08 2011 11:16 jalstar wrote:On April 08 2011 11:14 space_yes wrote:![[image loading]](http://i55.tinypic.com/332w3sn.jpg) Not sure what to tell you. The poll only tricks people b/c the fraction is written on one line instead of being formatted so you have to use order of operations.. Writing it on one line is the trick. It's bad notation and confusing at first glance. That book writes it on two lines, which is the proper way to do it. I am now going to assume you don't know what ambiguity is. "Confusing" is not ambiguity if the cause of the confusion is ignorance (or even just not reading correctly). On April 08 2011 11:16 MadVillain wrote:On April 08 2011 11:13 Zeke50100 wrote:On April 08 2011 11:11 jalstar wrote:On April 08 2011 11:10 Zeke50100 wrote:On April 08 2011 11:08 jalstar wrote:On April 08 2011 11:07 Zeke50100 wrote:On April 08 2011 11:06 jtan wrote:
There also seems to be some different use of the word ambigous.
The expression 1/x*y is unambigious in the strict computer-sience sense, but like I said, it's ambigious in the sense that a lot of people interpret it differently, you can't really argue against that. Lack of knowledge does not mean ambiguous. Are you really trying to argue that hundreds of people don't know order of operations, or am I missing something? Yes. Hundreds of people (those who have bothered to reply, anyway, which is indicative of response bias in the first place) just don't know their stuff. You can't be serious. I just refuse to believe you're serious. You really can't see how the problem is a trick without assuming complete lack of order of operations knowledge? What the fuck? I never said a complete lack of knowledge. You might want to look up what knowledge means. Somebody's ignorance of the fact that you do not, indeed, multiply 2 by 9+3 before proceeding with the rest of the simplification is a lack of knowledge. But that is not why people got the question wrong. They got it wrong because they assumed that 2(9+3) is being used as a single unit which it often is in a mathematical setting. Nobody was lacking the knowledge of order of operations as you're claiming. Face it, by definition the question is ambiguous. I'll post the definition again in case you missed it: "Ambiguity is a term used in writing and math, and under conditions where information can be understood or interpreted in more than one way..." People "interpreted" the 2(9+3) to be one unit it can also be interpreted as not being one unit. There are two ways to interpret it. Two is more that one. It is ambiguous. Clear? I don't think you have the "knowledge" of what ambiguity is. The definition of ambiguity you used is a vague, broad definition that only serves to include pretty much anything you want. I interpret 2+2 to equal 5. To hell with it, it's an ambiguous question. 2(9+3) isn't a single term. Even if it is, that would mean 288 is simply wrong, not that the question itself is ambiguous. What? So you're just disregarding my definition of ambiguity, which is the definition wikipedia gives by the way? I didn't say 288 was wrong, the definition says nothing about whether the information that is being interpreted leads to a correct answer or not, it simply says that if it can be interpreted in more than one way it is ambiguous, really it's very simple. 288 is the correct answer, but the question is ambiguous. And you're example is completely off base and shows you don't understand the definition of ambiguous. First of all 2+2 = 5 isn't a question, it is a mathematical statement which is clearly incorrect. You're disregarding the rest of wikipedia's definition of ambiguity. Ambiguity is a term used in writing and math, and under conditions where information can be understood or interpreted in more than one way and is distinct from vagueness, which is a statement about the lack of precision contained or available in the information.The question is vague because the notation is imprecise by text-book standards.
QFT before this gets lost. There you go. The question is vague but not ambiguous. Simple as that.
Edit: Not that people will admit they're wrong, even if it is the dictionary disagreeing with them. Sigh.
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On April 08 2011 11:38 jalstar wrote:Show nested quote +On April 08 2011 11:35 naptiem wrote:
I don't know why some mathematicians would be so loose in defining their notations. I understand that it is easy to think of these in terms of natural groupings. But rigorously, they are not. Seems to border on trolling when WolframAlpha shows the correct and unambiguous result. Wolfram Alpha gives the incorrect result for 1/xy and 1/2x.
It does show a difference between 1/2x and 1/2 x. I take back what I obviously said without any fact checking. Keep thinking of 2x as a natural grouping and apply it with abandon.
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Fine, if you want to get semantic, it's a vague question. But multi-valued functions aren't ambiguous, I can't believe someone suggested that.
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On April 08 2011 11:38 Zeke50100 wrote:AN EXAMPLE OF AN AMBIGUOUS QUESTION:What is the square-root of 4? See how that's ambiguous? See how it cannot compare to the OP's poll-question? Show nested quote +On April 08 2011 11:38 shinosai wrote:On April 08 2011 11:35 Zeke50100 wrote:On April 08 2011 11:34 shinosai wrote:On April 08 2011 11:23 StarStruck wrote:On April 08 2011 11:09 shinosai wrote:
Hmm. I got it wrong, but I'm not really bothered by it. My calculus book never had such poor notation. Parenthesis are your friend. I think this thread really just amounts to people being annoyed by bad notation (not necessarily wrong, but bad nonetheless). In the math classes that I took, using parenthesis to make your work clear and concise was mandatory. That's calculus though. When you see a problem written in the following you have to ask yourself. What is this problem asking? There are only 3 things. Brackets, division and multiplication. What does this tell you? One of the first things you learned about operations. What you see is what you get. Poor form or not. Sure, it's poor form to the scholarly eye, but you should have an idea of what they're asking based on the shitty form alone. There's a reason why you don't see ÷ used so much anymore! That's like the first indication. Grade school math. Order of operations! :O The fact you guys are saying it's ambiguous should tell you it's an elementary question asking you to use the order of operations. I didn't say it was ambiguous, but it is bad notation. Now, I know you think this should make me feel bad because this is grade school math. However, it doesn't, because the practical application of bad notation is zero. What I'm trying to say is, bad notation like this is something you will almost never come across. It's like making fun of someone for misinterpreting an English sentence that was written with an odd word order. We come across these all the time, and instead of making fun, why not just clarify by writing in standard word order? I'm never going to have to apply trigonometric identities in real life. Does that mean I should ignore its existence? Trigonometric identities have useful functions for solving problems. Please detail me on what exactly is useful about bad notation in comparison to standard notation? This is one that I would love to hear. I never said bad notation was useful. You, however, are saying that you shouldn't need to know bad notation at all, essentially ignoring that it is completely legitimate and legal.
sqrt(4) = 2 with no ambiguity what so ever
what are you talking about??
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On April 08 2011 11:42 jalstar wrote:Show nested quote +On April 08 2011 11:38 Zeke50100 wrote:
AN EXAMPLE OF AN AMBIGUOUS QUESTION:
What is the square-root of 4?
See how that's ambiguous? See how it cannot compare to the OP's poll-question?
Ok, you don't know what ambiguous means. Hint: it doesn't mean "multi-valued".
Methinks you don't know what it means. It can be interpreted as +2, -2, +2/-2, or as an invalid question.
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On April 08 2011 11:34 jtan wrote:
zeke, space_yes, jalstar and all of you arguing this, how much math did you take?
Just curious...
I'm a Comp Sci & Chem E major at University of Minnesota, I've taken: Multivariable Calc, Linear Algebra, An introductory course to Combinatorics/Set Theory/A couple other things, Numerical Analysis.. some others
only a sophmore though so I have a lot ahead
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On April 08 2011 11:37 MadVillain wrote:Show nested quote +On April 08 2011 11:32 Zeke50100 wrote:On April 08 2011 11:29 MadVillain wrote:On April 08 2011 11:25 phantaxx wrote:On April 08 2011 11:16 MadVillain wrote:On April 08 2011 11:13 Zeke50100 wrote:On April 08 2011 11:11 jalstar wrote:On April 08 2011 11:10 Zeke50100 wrote:On April 08 2011 11:08 jalstar wrote:On April 08 2011 11:07 Zeke50100 wrote:
[quote]
Lack of knowledge does not mean ambiguous. Are you really trying to argue that hundreds of people don't know order of operations, or am I missing something? Yes. Hundreds of people (those who have bothered to reply, anyway, which is indicative of response bias in the first place) just don't know their stuff. You can't be serious. I just refuse to believe you're serious. You really can't see how the problem is a trick without assuming complete lack of order of operations knowledge? What the fuck? I never said a complete lack of knowledge. You might want to look up what knowledge means. Somebody's ignorance of the fact that you do not, indeed, multiply 2 by 9+3 before proceeding with the rest of the simplification is a lack of knowledge. But that is not why people got the question wrong. They got it wrong because they assumed that 2(9+3) is being used as a single unit which it often is in a mathematical setting. Nobody was lacking the knowledge of order of operations as you're claiming. Face it, by definition the question is ambiguous. I'll post the definition again in case you missed it: "Ambiguity is a term used in writing and math, and under conditions where information can be understood or interpreted in more than one way..." People "interpreted" the 2(9+3) to be one unit it can also be interpreted as not being one unit. There are two ways to interpret it. Two is more that one. It is ambiguous. Clear? I don't think you have the "knowledge" of what ambiguity is. If I interpret 2+4 * 6 as (2+4) * 6, that doesn't mean it is ambiguous. I would just be wrong. But under no mathematical setting do people ever interpret 2+4*6 to be (2+4) * 6, that is a silly facetious example. Do you actually think that people in a university setting interpret 1/xy as (1/x)*y ? No, they don't. The ambiguity arises from the fact that 2(9+3) is commonly viewed as a single unit, just as xy is. Under no mathematical setting? Guess what? He just did. EDIT: You think universities don't recognize 1/xy as y/x? What university are you talking about? Ok you're clearly being flippant, how can you reasonably say that the general population would view 2+4*6 as (2+4)*6? The second poll in this post CLEARLY shows that people interpret things differently. He just made that example up for sake of his poorley executed argument. The general population, especially in a mathematical setting in a university would NEVER view the statement like that.
It doesn't matter how reasonable it is to interpret it in a different way, whether or not something is ambiguous is not a measurement of how often it gets interpreted differently, it either is or is not based on whether or not there are multiple correct interpretations. In my example and in OP there is only one correct interpretation, so it is irrelevent how many people interpret it differently it is still not ambiguous.
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On April 08 2011 11:44 Zeke50100 wrote:Show nested quote +On April 08 2011 11:42 jalstar wrote:On April 08 2011 11:38 Zeke50100 wrote:
AN EXAMPLE OF AN AMBIGUOUS QUESTION:
What is the square-root of 4?
See how that's ambiguous? See how it cannot compare to the OP's poll-question?
Ok, you don't know what ambiguous means. Hint: it doesn't mean "multi-valued". Methinks you don't know what it means. It can be interpreted as +2, -2, +2/-2, or as an invalid question.
Actually, sqrt isn't multi-valued, it's strictly positive. "What number, when squared, equals four?" gives you +/- 2.
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On April 08 2011 11:38 mcc wrote:Show nested quote +On April 08 2011 11:07 Zeke50100 wrote:On April 08 2011 11:06 jtan wrote:
There also seems to be some different use of the word ambigous.
The expression 1/x*y is unambigious in the strict computer-sience sense, but like I said, it's ambigious in the sense that a lot of people interpret it differently, you can't really argue against that. Lack of knowledge does not mean ambiguous. Problem is when none uses the rule in practice, which from my experience is the case of 1/xy. My math professors used (as seldom as they used one line notation) 1/xy as meaning 1/(xy), even though everyone knew that it is not correct according to the order of operations rule. So if you asked people there what 1/xy means the answer 1/xy = 1/(xy) would be correct as universal usage supersedes not used rule and creates new variant of the notation. I would assume a lot of math communities use it the same way ? So when OP asks his question and does not specify notation it is in fact ambiguous. You cannot always assume everyone uses the same notation. If you write (48/2)(9+3) you can assume reasonably that everyone's notation interprets it correctly. In case of OP's formulation, that assumption gets much weaker.
what you say might be true but it is not a formal notation as far as i know and when you seek to communicate with people you generally follow the standards, which is, again as far as i know, the order of operations. it's a bit of a tricky question and people who got 2 made a little mistake reading the equation but that doesn't mean the equation was written incorrectly nor does it make the equation ambiguous unless you can apply another formal set of notations to that equation that would make sense.
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EPT
