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On April 08 2011 11:29 MadVillain wrote:Show nested quote +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: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. 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?
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On April 08 2011 11:25 MadVillain wrote:Show nested quote +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.
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You guys if the OP put parentheses in the question so it was (1/2)x it wouldn't be a trick question and the entire thread would be pointless and stupid. Going on about "bad presentation" or whatever is silly when the entire point of the thread is see how many people get the first question right but get the second question wrong.
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On April 08 2011 11:23 StarStruck wrote:Show nested quote +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?
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zeke, space_yes, jalstar and all of you arguing this, how much math did you take?
Just curious...
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On April 08 2011 11:29 Zeke50100 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: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. I use ambiguous wording myself. The "question" I was referring to (implying, really) was "what is 2+2?" Anybody can interpret anything to mean anything they want, and the wikipedia definition really doesn't give justice to context. To me, the question in the OP is clearly 288. Simply saying that would completely crush your argument, but I can't live with that because nobody would respect that as a proper response  I definitely understand the definition of ambiguity. The example I posted was to prove how terrible the definition was in the first place.
If you understand the definition of ambiguity than you should see that the mathematical statement IS ambiguous. Maybe you should give your own definition of ambiguity because all the dictionaries and common usages of ambiguous that I've found define it in this same way: If something can be REASONBLY be interpreted in more than one way than it is ambiguous. Nobody would reasonably interpret "Does 2+2=5?" As ambiguous because there is little room for syntactical, grammatical or whatever differences. I saw 2(9+3) as being treated as one unit, simply because in university math setting it is often shown that way. I'm not denying that it would give you the wrong answer, it does. What I'm saying is that it is ambiguous, and says nothing of the correctness that the interpretation gives.
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On April 08 2011 11:28 jalstar wrote:Show nested quote +On April 08 2011 11:27 Mailing wrote:
ok, question
48
-------- = x
2(9+3)
48 = x(2(9+3))
48 = x(2(12))
48 = x(24)
x = 2
Why is this mathematically incorrect? It's not, but that's not what the OP's problem is asking.
But they ARE saying what I did was wrong, and that the TRUE ONE correct answer is 288, i just want to know why and what I did is wrong.
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United States10328 Posts
So I just polled some more MIT math/physics majors. One said 288, one said 2, and one (who was incidentally top 14 on the Putnam exam...) said 72 because he hasn't seen a division sign written like that in years and thought it was a plus sign.
I think the problem is that when the division sign is written that way, people who do math automatically convert it to a fraction bar--after all, that's what ÷ means: the dots represent expressions and the -- is a fraction bar.
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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.
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On April 08 2011 11:34 shinosai wrote:Show nested quote +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?
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On April 08 2011 11:27 Mailing wrote:
ok, question
48
-------- = x
2(9+3)
48 = x(2(9+3))
48 = x(2(12))
48 = x(24)
x = 2
Why is this mathematically incorrect?edit - doh
Because it isn't the same question.
You are pairing [2(9+3)] when that isn't the case.
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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.)
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holy shit... i couldnt even get the result 2 even i wanted to...
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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...
Linear Algebra, Real Analysis, Differential Equations, Nonlinear Dynamics, Game Theory, and Complex Analysis, all at UCLA.
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On April 08 2011 11:32 timothyarm wrote:Show nested quote +On April 08 2011 11:29 MadVillain wrote:
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.
This.
ok, you see, now we really are getting into semantics. just because something can be misinterpreted doesn't make it ambiguous. if something is ambiguous it specifically allows for more than one interpretation.
if a sign said no parking from 6:00-8:00 it would be ambiguous because it doesn't specify am or pm or date.
if a sign said no parking from 6:00pm-8:00pm mon-fri but doesn't say tell you the time zone it doesn't make it ambiguous because you can interpret it to be in a different time zone.
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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.
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On April 08 2011 11:27 Mailing wrote:
ok, question
48
-------- = x
2(9+3)
48 = x(2(9+3))
48 = x(2(12))
48 = x(24)
x = 2
Why is this mathematically incorrect?
That isn't incorrect, it's not the same as what the OP asked for though. The fraction bar regroups the terms. What you wrote is evaluated the same way as 48 / (2 (9 + 3)) = x.
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On April 08 2011 11:32 Zeke50100 wrote:Show nested quote +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: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. 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.
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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.
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EPT
