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On April 08 2011 11:41 timothyarm wrote:
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.
Asking the question across different demographics would be very interesting. I think I'm much more likely to get the question right b/c I'm studying math and I frequent discussion boards where expressions like 1/2x are quite common.
edit: though to be fair, I would write the expression as (1/2)x for additional clarity
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On April 08 2011 11:46 mahnini wrote:Show nested quote +On April 08 2011 11:38 mcc 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. 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.
Not incorrectly, but poorly, since 2(9+3) looks like a grouping and it isn't.
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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, no. It's 2.
Go read a math book.
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On April 08 2011 11:47 jalstar wrote:Show nested quote +On April 08 2011 11:46 mahnini wrote:On April 08 2011 11:38 mcc 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. 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. Not incorrectly, but poorly, since 2(9+3) looks like a grouping and it isn't.
yes, it can be written better but it is also perfectly readable in it's current form.
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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.
No that isn't what it means. The correct answer isn't the "interpretation" that the definition is referring to. The interpretation refers to what the question is asking and whether it can reasonably be thought that the question may be asking something else.
"What is the square-root of 4?" cannot be interpreted as meaning anything but "give the square root of 4"
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On April 08 2011 11:47 jtan wrote:Show nested quote +On April 08 2011 11:44 Zeke50100 wrote: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, no. It's 2. Go read a math book.
sqrt(x^2) = +/-x, does it not? :-)
Okay, I won't erase that, but...I'll correct what I meant. Lol.
(-x)^2 = (x)^2 = x^2
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On April 08 2011 11:23 Zeke50100 wrote:Show nested quote +On April 08 2011 11:19 abaDURRR wrote:
When i see a divide sign, i interpret it as thing on the left over thing on the right
So I ended up with
_48_
2(9+3)
Which ends with the answer 2 ...So, as soon as you see a division sign, you immediately stick EVERYTHING to the right of it in the denominator if it's not offset by parentheses? >.>
Ok that was a bad way to explain it.
When i saw the question, I distributed the 2 into the (9+3) which makes me end up with 48/24.
Everyone saying that this question was poorly written is correct, the * in 48/2*(9+3) would make a world of difference
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On April 08 2011 11:47 jtan wrote:Show nested quote +On April 08 2011 11:44 Zeke50100 wrote: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, no. It's 2. Go read a math book.
I never said "principal square root".
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On April 08 2011 09:20 buhhy wrote:Show nested quote +On April 08 2011 09:18 Severedevil wrote:
No one would interpret 48 / 2 * (9+3) as anything but 24 * 12 = 288, or 1 / 2 * x as anything but x/2. However, when you use juxtaposition to sub for multiplication, it is frequently understood that you are collecting 2(9+3) or 2x into one unit. This. Now, can someone post the bodybuilding link? Why did it get removed?
Sup.
There were over a dozen. And there's new ones now too, but they got removed for the 228 crew and the 2 crew took turns calling each other phaggots.
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The first makes total sense. I study statistics/ business economics, so kinda math but not really a STEM field. The second I think means 1 ÷ 2x, but I'm unsure.
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On April 08 2011 11:49 timothyarm wrote:Show nested quote +On April 08 2011 11:47 jtan wrote:On April 08 2011 11:44 Zeke50100 wrote: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, no. It's 2. Go read a math book. sqrt(x^2) = +/-x, does it not? :-) Okay, I won't erase that, but...I'll correct what I meant. Lol. (-x)^2 = (x)^2 = x^2
sqrt(x^2) = |x| for all real x, no ambiguity in any case. Maybe this should have been the poll also as there seems to be some different opinions 
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On April 08 2011 11:48 MadVillain wrote:Show nested quote +On April 08 2011 11:44 Zeke50100 wrote: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. No that isn't what it means. The correct answer isn't the "interpretation" that the definition is referring to. The interpretation refers to what the question is asking and whether it can reasonably be thought that the question may be asking something else. "What is the square-root of 4?" cannot be interpreted as meaning anything but "give the square root of 4"
I'll actually concede this. It was a vague question, rather than ambiguous.
An ambiguous question would be "What is f(x)".
However, the OP's question is still not ambiguous, because 2(9+3) is not a single term >.>
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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.
You made an analogy comparing bad notation to something useful. I thought it was clear that you thought bad notation was useful. My bad.
And since it is not practically useful, I'm not sure why it being legitimate and legal is relevant. I'm sure there are a lot of things in this world that are legitimate and legal that you and I both don't have a care in the world about. I fail to see why I should feel any worse about misinterpreting a poorly notated math problem than misinterpreting a poorly ordered English sentence. Both happen occasionally, but neither are necessary for a high level understanding of mathematics or English.
Anyways, your argument mostly seems to stem from the fact that you think people have a problem understanding order of operations, but mostly people just have a problem with the grouping notation. I understand the order of operations perfectly fine, and given standard notation, would never have an issue solving such a problem. Given that standard notation is, well, standard, I fail to see the importance of this legitimate, legal, and useless "bad" notation.
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On April 08 2011 11:50 Zeke50100 wrote:Show nested quote +On April 08 2011 11:47 jtan wrote:On April 08 2011 11:44 Zeke50100 wrote: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, no. It's 2. Go read a math book. I never said "principal square root".
Haha this is interesting. You unknowngly gave an ambiguous question (though only in this situation) most people interpret "What is the square-root of x?" To mean principal square root, you obviously interpret that question as "What are ALL the square roots of x?" THAT is ambiguous, same thing as the OP's question just written in words not math.
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On April 08 2011 11:50 Zeke50100 wrote:Show nested quote +On April 08 2011 11:47 jtan wrote:On April 08 2011 11:44 Zeke50100 wrote: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, no. It's 2. Go read a math book. I never said "principal square root".
Solving x^2 = 4 gives two answers, x = 2 or -2
Evaluating ![[image loading]](http://upload.wikimedia.org/math/d/4/a/d4a83a46eba9ba4adce2448d0f30985e.png) gives only one answer, 2
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Really don't see a problem in this :S?
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On April 08 2011 11:53 shinosai 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? 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. You made an analogy comparing bad notation to something useful. I thought it was clear that you thought bad notation was useful. My bad. And since it is not practically useful, I'm not sure why it being legitimate and legal is relevant. I'm sure there are a lot of things in this world that are legitimate and legal that you and I both don't have a care in the world about. I fail to see why I should feel any worse about misinterpreting a poorly notated math problem than misinterpreting a poorly ordered English sentence. Both happen occasionally, but neither are necessary for a high level understanding of mathematics or English. Anyways, your argument mostly seems to stem from the fact that you think people have a problem understanding order of operations, but mostly people just have a problem with the grouping notation. I understand the order of operations perfectly fine, and given standard notation, would never have a problem with such a thing. Given that standard notation is, well, standard, I fail to see the importance of this legitimate, legal, and useless "bad" notation.
This is the kind of argument players who lose to Bronze players in SC2 say to "cover their asses". It's not valid to say that something is nonstandard, therefore should not be given any significance. Everybody is expected to know that 2/2 is equal to 1, even if it's less standard to be written as 2/2.
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On April 08 2011 11:52 jtan wrote:Show nested quote +On April 08 2011 11:49 timothyarm wrote:On April 08 2011 11:47 jtan wrote:On April 08 2011 11:44 Zeke50100 wrote: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, no. It's 2. Go read a math book. sqrt(x^2) = +/-x, does it not? :-) Okay, I won't erase that, but...I'll correct what I meant. Lol. (-x)^2 = (x)^2 = x^2 sqrt(x^2) = |x| for all real x, no ambiguity in any case. Maybe this should have been the poll also as there seems to be some different opinions
'sqrt' is the principal square root function. It is not 'the' square root of a positive number... it is ONE of the TWO square roots of a positive number. Specifically, it's the positive one.
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LOL I'm in high school and got this right ROFL.
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On April 08 2011 11:53 MadVillain wrote:Show nested quote +On April 08 2011 11:50 Zeke50100 wrote:On April 08 2011 11:47 jtan wrote:On April 08 2011 11:44 Zeke50100 wrote: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, no. It's 2. Go read a math book. I never said "principal square root". Haha this is interesting. You unknowngly gave an ambiguous question (though only in this situation) most people interpret "What is the square-root of x?" To mean principal square root, you obviously interpret that question as "What are ALL the square roots of x?" THAT is ambiguous, same thing as the OP's question just written in words not math.
I actually didn't realize this, so...
IT WAS INTENDED! 
Although still, people said the square-root of 4 was ONLY 2, which is only true if you accept that it is the principal square root I'm asking for.
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EPT
