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On April 08 2011 09:34 mahnini wrote:Show nested quote +On April 08 2011 09:24 -{Cake}- wrote:
Mathematical/linguistic rules are not a good way to justify correctness. (meaning pedmas or w/e is not an acceptable defense)
Notation is subjective, there is no such thing as correct or incorrect notation. You can redefine any convention, notation, language, etc in any way you want because they are all arbitrary constructs to begin with
If you're personally solving the problem, you can use 48&2@9#3 or w\jx(ptE) or even weiogheroighjtoh940tiuojeithdiohj5hj if you like
If you do not know your target audience, using massive amounts of parenthesis ((48)/(2))*(9+3) is more likely to result in your idea being communicated successfully, but that doesn't make it more correct
Either answer can be correct depending on how individuals interpret the expression, because under different conventions, the expression means different things that is poppycock if the equation was 4 + 5 * 3 no one would answer 27 and argue it was the correct answer because people would follow the order of operations. i don't get why people are getting so defensive about it, it's a tricky question which tests your understanding of the order of operations, there's no need to bring relativism into this.
It was an exaggerated example because while 288 is 'formally' correct, if the expression were written informally, a decent amount of people would interpret it as 2 (clearly), and they would be correct within that system.
maybe that's a little more clear? =/
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What's the big deal here?
I have taken a compiler class it's all disambiguation of different parse trees.
Depend on your grammar....
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I think the title is hugely misleading.
It should be
a simple parse problem
The math is easy after we parse it. So it all depends on what's your grammar and how do you parse with it.
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On April 08 2011 09:47 bootbootcar wrote:Show nested quote +On April 08 2011 09:38 iNSiPiD1 wrote:
The issue with this thread is that mathematics should never be written in the form described by the OP. I just wrote a 23 page math paper for my B.S. in math, and it's just misleading to assume that because people cannot interpret the form given by the OP that they suck at math.
I argue only those who know very little about math would be concerned over something as trivial as someone getting the answer to this wrong. For those who appreciate math would know to add an extra set of parenthesis, in order to make our meaning as unambiguous as possible. It's all about elegance of presentation.
Kind of OT, but I've always been wondering, what kind of papers do Math majors write? Don't most mathematical facts already have proofs?
No. 
There is a lot of grunt work to do, and also a lot of really hard and high level problems that need to be proven, disproven or it needs to be proven that the problem cannot be proven in given axiomatic system.
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On April 08 2011 09:51 evanthebouncy! wrote:
What's the big deal here?
I have taken a compiler class it's all disambiguation of different parse trees.
Depend on your grammar....
Modern mathematics doesn't use more than one grammar...
edit: by convention
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On April 08 2011 09:22 Zeke50100 wrote:Show nested quote +On April 08 2011 09:03 munchmunch wrote:On April 08 2011 08:59 Zeke50100 wrote:On April 08 2011 08:52 garbanzo wrote:On April 08 2011 08:50 Mailing wrote:On April 08 2011 08:49 Zeke50100 wrote:On April 08 2011 08:47 garbanzo wrote:On April 08 2011 08:39 Zeke50100 wrote:On April 08 2011 08:38 Entropic wrote:
lol what a shittily written and ambiguous expression (as many have noted already) It's 0% ambiguous, but 100% a test of your understanding of math. You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)? How about 1/2(a+b) versus 1/2*(a+b)? There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity. If you can find some evidence of this.. Yes, I would like some source that it can definitively only be read one way. And you didn't really answer my question. If you were to ask someone a question, and you wanted absolutely no confusion, then would you consider choosing one notation over the other? I think you're lying to yourself if you say otherwise. I don't get how "these two things are exactly the same" do not equate to "these two things are interchangeable, and therefore one is no more ambiguous than the other" in your mind. LOL, I read that and thought "What a good post, well said!" Then I reread it and realized you were saying the exact opposite of what I thought. I guess a Zeke50100 is an anti-munchmunch. And to jump into that conversation, "the same" on a semantic level is not the same as being "the same" on a syntactic level. Syntax doesn't mean a thing when it comes to ambiguity because it should be understood that both are simplified to the same level. You're suggesting that "2+1-1" would be more correct than "2-1+1" because it's syntactically more "natural" to somebody's own perception, which is what garbanzo is trying to say.
Of course syntax means something when it comes to ambiguity. People who write programming language specifications have to think about syntactic ambiguity all the time. And syntactic ambiguity is by definition the ambiguities that occur before or in the process of simplification.
The fact that neither "2+1-1" and "2-1+1" are neither syntactically or semantically ambiguous to most people has nothing to do with it. I agree that one is more natural than the other, but in my mind this is a third concept distinct from ambiguity or correctness (which are themselves very distinct).
Anyway, I have to quit the thread now. Nice talking to you... quite fun when I'm procrastinating to meet somebody who can write well but thinks exactly the opposite to myself.
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On April 08 2011 09:53 evanthebouncy! wrote:
I think the title is hugely misleading.
It should be
a simple parse problem
The math is easy after we parse it. So it all depends on what's your grammar and how do you parse with it.
winning
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On April 08 2011 09:44 shabinka wrote:Show nested quote +On April 08 2011 09:23 space_yes wrote:On April 08 2011 08:43 DTK-m2 wrote:
Alright guys, it's a very simple solution.
If you're considering machine communication, then any computer or calculator would interpret 1/2x as "x/2." Just put it in your calculator right now. If I pick up my TI-83 and input "1/2*3", it will put the 3 in the numerator. That would be the "correct" answer if it's the context in which we are doing these math problems.
If you're considering human communication, where someone is just trying to convey a question to someone else, then the question asker must be more specific. Seriously, just add a single set of parentheses. He's being unnecessarily ambiguous.
EDIT: Ah, I did not know WolframAlpha did that. Then it that case, even machines will interpret this differently. In any case, I would add parentheses to be safe. You get the result you do b/c machine parsing puts each element into a stack and using reverse polish notation creates a syntax tree. Wolfram Alpha is a special case b/c it's designed for...newbies (see poll results) . If you put in "1/2 x": ![[image loading]](http://i52.tinypic.com/214a03o.png) Note the space in the above. Now before everyone who got the second question wrong jumps in and argues Wolfram Alpha's parsing of the expression with a space validates their interpretation understand that machine parsing isn't evidence for anything. If you use Mathematica with spaces you get: ![[image loading]](http://i51.tinypic.com/uc8pi.png) With no spaces: ![[image loading]](http://i52.tinypic.com/mr3cr4.png) Generally most machines will interpret the expression as above. I don't have the symbolic computing package for Matlab on the computer I'm currently using but I believe it interprets 1/2x the same way Mathematica does. There is no ambiguity; the question tests whether you understand order of operations. If you got the first question correct you should get the second one right also if you apply the same rules + Show Spoiler + There are no parenthetical expressions so you can just start working left to right. Divide 1 by 2. Now you have .5x. http://www.wolframalpha.com/input/?i=1/2xI'm sorry.
We were discussing why Wolfram Alpha interprets 1/2x as 1/(2x) whereas 1/2 x is .5x. Please take the time to fully read my post and prior conversation before posting. Thanks.
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On April 08 2011 09:54 munchmunch wrote:Show nested quote +On April 08 2011 09:22 Zeke50100 wrote:On April 08 2011 09:03 munchmunch wrote:On April 08 2011 08:59 Zeke50100 wrote:On April 08 2011 08:52 garbanzo wrote:On April 08 2011 08:50 Mailing wrote:On April 08 2011 08:49 Zeke50100 wrote:On April 08 2011 08:47 garbanzo wrote:On April 08 2011 08:39 Zeke50100 wrote:On April 08 2011 08:38 Entropic wrote:
lol what a shittily written and ambiguous expression (as many have noted already) It's 0% ambiguous, but 100% a test of your understanding of math. You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)? How about 1/2(a+b) versus 1/2*(a+b)? There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity. If you can find some evidence of this.. Yes, I would like some source that it can definitively only be read one way. And you didn't really answer my question. If you were to ask someone a question, and you wanted absolutely no confusion, then would you consider choosing one notation over the other? I think you're lying to yourself if you say otherwise. I don't get how "these two things are exactly the same" do not equate to "these two things are interchangeable, and therefore one is no more ambiguous than the other" in your mind. LOL, I read that and thought "What a good post, well said!" Then I reread it and realized you were saying the exact opposite of what I thought. I guess a Zeke50100 is an anti-munchmunch. And to jump into that conversation, "the same" on a semantic level is not the same as being "the same" on a syntactic level. Syntax doesn't mean a thing when it comes to ambiguity because it should be understood that both are simplified to the same level. You're suggesting that "2+1-1" would be more correct than "2-1+1" because it's syntactically more "natural" to somebody's own perception, which is what garbanzo is trying to say. Of course syntax means something when it comes to ambiguity. People who write programming language specifications have to think about syntactic ambiguity all the time. And syntactic ambiguity is by definition the ambiguities that occur before or in the process of simplification. The fact that neither "2+1-1" and "2-1+1" are neither syntactically or semantically ambiguous to most people has nothing to do with it. I agree that one is more natural than the other, but in my mind this is a third concept distinct from ambiguity or correctness (which are themselves very distinct). Anyway, I have to quit the thread now. Nice talking to you... quite fun when I'm procrastinating to meet somebody who can write well but thinks exactly the opposite to myself.
Funny you should mention that, since I should probably do some work myself  It's easily possible that somebody finds 2+1-1 more ambiguous to 2-1+1, which is something along the lines of what I was trying to say; however, that doesn't make one of them more ambiguous in the grand scheme of things (both being expressions of equal length and all).
Anyway, with those of you saying that it would be correct in an informal setting, the problem is that this is on the internet, where an "informal" (which you should really call oral or face-to-face communication via speaking) setting is impossible in the same way sending sarcasm through text without tone is impossible. When typing, we have to assume robotic rule-following, rather than what would "normally" occur when two people communicate.
Also, the reason certain languages do not accept parentheses as a function in itself is not a flaw in math, but a flaw in the language itself ^_^
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the problem with the 2nd poll, is that as a computer programmer, i see 1/2, as 1, divided by 2, not as a half :/. Question needs reformatting.
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On April 08 2011 09:50 -{Cake}- wrote:Show nested quote +On April 08 2011 09:34 mahnini wrote:On April 08 2011 09:24 -{Cake}- wrote:
Mathematical/linguistic rules are not a good way to justify correctness. (meaning pedmas or w/e is not an acceptable defense)
Notation is subjective, there is no such thing as correct or incorrect notation. You can redefine any convention, notation, language, etc in any way you want because they are all arbitrary constructs to begin with
If you're personally solving the problem, you can use 48&2@9#3 or w\jx(ptE) or even weiogheroighjtoh940tiuojeithdiohj5hj if you like
If you do not know your target audience, using massive amounts of parenthesis ((48)/(2))*(9+3) is more likely to result in your idea being communicated successfully, but that doesn't make it more correct
Either answer can be correct depending on how individuals interpret the expression, because under different conventions, the expression means different things that is poppycock if the equation was 4 + 5 * 3 no one would answer 27 and argue it was the correct answer because people would follow the order of operations. i don't get why people are getting so defensive about it, it's a tricky question which tests your understanding of the order of operations, there's no need to bring relativism into this. It was an exaggerated example because while 288 is 'formally' correct, if the expression were written informally, a decent amount of people would interpret it as 2 (clearly), and they would be correct within that system. maybe that's a little more clear? =/
Correctness in a poorly defined "informal" system is meaningless.
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On April 08 2011 09:38 iNSiPiD1 wrote:
I just wrote a 23 page math paper for my B.S. in math, and it's just misleading to assume that because people cannot interpret the form given by the OP if they suck at math.
I argue only those who know very little about math would be concerned over something as trivial as someone getting the answer to this wrong. For those who appreciate math would know to add an extra set of parenthesis, in order to make our meaning as unambiguous as possible. It's all about elegance of presentation.
Fixed. :p
As for the second part. I disagree. I believe the main reason why some of you are getting it wrong is because you are over-thinking and not using the basics you were taught way back when.
If you look at any skill testing question at McDonalds or any othe fast food restaurant you would find similar mathematical problems. Throw the algebra out the window and keep it simple.
You cannot add something that isn't there. That changes the problem and the solution completely.
Think back to your grade school textbooks. You would never ever do that.
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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.
If this was a question on order of operations, you'd actually give a question that had syntactically correct statement. In particular, I don't believe that xy = x*y or (x*y) is generally defined in most things I've seen, so it's generally up to the person to interpret.
I'm shocked that the OP has only just a poll and not some point otherwise., otherwise this is like trolling all of us.
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On April 08 2011 10:02 Zeke50100 wrote:Show nested quote +On April 08 2011 09:54 munchmunch wrote:On April 08 2011 09:22 Zeke50100 wrote:On April 08 2011 09:03 munchmunch wrote:On April 08 2011 08:59 Zeke50100 wrote:On April 08 2011 08:52 garbanzo wrote:On April 08 2011 08:50 Mailing wrote:On April 08 2011 08:49 Zeke50100 wrote:On April 08 2011 08:47 garbanzo wrote:On April 08 2011 08:39 Zeke50100 wrote:
[quote]
It's 0% ambiguous, but 100% a test of your understanding of math. You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)? How about 1/2(a+b) versus 1/2*(a+b)? There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity. If you can find some evidence of this.. Yes, I would like some source that it can definitively only be read one way. And you didn't really answer my question. If you were to ask someone a question, and you wanted absolutely no confusion, then would you consider choosing one notation over the other? I think you're lying to yourself if you say otherwise. I don't get how "these two things are exactly the same" do not equate to "these two things are interchangeable, and therefore one is no more ambiguous than the other" in your mind. LOL, I read that and thought "What a good post, well said!" Then I reread it and realized you were saying the exact opposite of what I thought. I guess a Zeke50100 is an anti-munchmunch. And to jump into that conversation, "the same" on a semantic level is not the same as being "the same" on a syntactic level. Syntax doesn't mean a thing when it comes to ambiguity because it should be understood that both are simplified to the same level. You're suggesting that "2+1-1" would be more correct than "2-1+1" because it's syntactically more "natural" to somebody's own perception, which is what garbanzo is trying to say. Of course syntax means something when it comes to ambiguity. People who write programming language specifications have to think about syntactic ambiguity all the time. And syntactic ambiguity is by definition the ambiguities that occur before or in the process of simplification. The fact that neither "2+1-1" and "2-1+1" are neither syntactically or semantically ambiguous to most people has nothing to do with it. I agree that one is more natural than the other, but in my mind this is a third concept distinct from ambiguity or correctness (which are themselves very distinct). Anyway, I have to quit the thread now. Nice talking to you... quite fun when I'm procrastinating to meet somebody who can write well but thinks exactly the opposite to myself. Funny you should mention that, since I should probably do some work myself It's easily possible that somebody finds 2+1-1 more ambiguous to 2-1+1, which is something along the lines of what I was trying to say; however, that doesn't make one of them more ambiguous in the grand scheme of things (both being expressions of equal length and all). Anyway, with those of you saying that it would be correct in an informal setting, the problem is that this is on the internet, where an "informal" (which you should really call oral or face-to-face communication via speaking) setting is impossible in the same way sending sarcasm through text without tone is impossible. When typing, we have to assume robotic rule-following, rather than what would "normally" occur when two people communicate. Also, the reason certain languages do not accept parentheses as a function in itself is not a flaw in math, but a flaw in the language itself ^_^
this a million times. this is what i was trying to get at with my you're vs your example (maybe not the best example anyway). in an "informal" situation you understand through context but this situation gives none and therefore you should default to accepted standards. maybe there are some set of rules in upper mathematics that trumps order of operations that i don't know, though no one has brought it up.
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Rofl I'm a math major and studying for my linear algebra test tmrw and i picked 2...brain too tired from matrix proofs to do simple math
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On April 08 2011 10:10 mahnini wrote:Show nested quote +On April 08 2011 10:02 Zeke50100 wrote:On April 08 2011 09:54 munchmunch wrote:On April 08 2011 09:22 Zeke50100 wrote:On April 08 2011 09:03 munchmunch wrote:On April 08 2011 08:59 Zeke50100 wrote:On April 08 2011 08:52 garbanzo wrote:On April 08 2011 08:50 Mailing wrote:On April 08 2011 08:49 Zeke50100 wrote:On April 08 2011 08:47 garbanzo wrote:
[quote]
You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)?
How about 1/2(a+b) versus 1/2*(a+b)? There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity. If you can find some evidence of this.. Yes, I would like some source that it can definitively only be read one way. And you didn't really answer my question. If you were to ask someone a question, and you wanted absolutely no confusion, then would you consider choosing one notation over the other? I think you're lying to yourself if you say otherwise. I don't get how "these two things are exactly the same" do not equate to "these two things are interchangeable, and therefore one is no more ambiguous than the other" in your mind. LOL, I read that and thought "What a good post, well said!" Then I reread it and realized you were saying the exact opposite of what I thought. I guess a Zeke50100 is an anti-munchmunch. And to jump into that conversation, "the same" on a semantic level is not the same as being "the same" on a syntactic level. Syntax doesn't mean a thing when it comes to ambiguity because it should be understood that both are simplified to the same level. You're suggesting that "2+1-1" would be more correct than "2-1+1" because it's syntactically more "natural" to somebody's own perception, which is what garbanzo is trying to say. Of course syntax means something when it comes to ambiguity. People who write programming language specifications have to think about syntactic ambiguity all the time. And syntactic ambiguity is by definition the ambiguities that occur before or in the process of simplification. The fact that neither "2+1-1" and "2-1+1" are neither syntactically or semantically ambiguous to most people has nothing to do with it. I agree that one is more natural than the other, but in my mind this is a third concept distinct from ambiguity or correctness (which are themselves very distinct). Anyway, I have to quit the thread now. Nice talking to you... quite fun when I'm procrastinating to meet somebody who can write well but thinks exactly the opposite to myself. Funny you should mention that, since I should probably do some work myself It's easily possible that somebody finds 2+1-1 more ambiguous to 2-1+1, which is something along the lines of what I was trying to say; however, that doesn't make one of them more ambiguous in the grand scheme of things (both being expressions of equal length and all). Anyway, with those of you saying that it would be correct in an informal setting, the problem is that this is on the internet, where an "informal" (which you should really call oral or face-to-face communication via speaking) setting is impossible in the same way sending sarcasm through text without tone is impossible. When typing, we have to assume robotic rule-following, rather than what would "normally" occur when two people communicate. Also, the reason certain languages do not accept parentheses as a function in itself is not a flaw in math, but a flaw in the language itself ^_^ this a million times. this is what i was trying to get at with my you're vs your example (maybe not the best example anyway). in an "informal" situation you understand through context but this situation gives none and therefore you should default to accepted standards. maybe there are some set of rules in upper mathematics that trumps order of operations that i don't know, though no one has brought it up.
48/2(9+3) has no multiplication operator.
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It looks like someone just forgot parentheses around 2(9+3), that's the trick I guess.
(48/2)(9+3) is well-posed, 48/(2(9+3)) is well posed, 48/2(9+3) is a trick question.
I want to write a math equation validator like the W3C one for web pages that returns "ambiguous use of parentheses error" when someone enters 48/2(9+3)
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edit: ^^^ posted first, pretty much said same thing.
2 and 288 is both correct, depends on interpretation.
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Honestly, I said the answer was 2 and I think the second problem is 1/(2*x) as well.
I'm not trying to be retarded here, but if you were to put that in front of me on a test back in my college days I would probably argue it to the death.
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On April 08 2011 10:14 Severedevil wrote:Show nested quote +On April 08 2011 10:10 mahnini wrote:On April 08 2011 10:02 Zeke50100 wrote:On April 08 2011 09:54 munchmunch wrote:On April 08 2011 09:22 Zeke50100 wrote:On April 08 2011 09:03 munchmunch wrote:On April 08 2011 08:59 Zeke50100 wrote:On April 08 2011 08:52 garbanzo wrote:On April 08 2011 08:50 Mailing wrote:On April 08 2011 08:49 Zeke50100 wrote:
[quote]
There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity. If you can find some evidence of this.. Yes, I would like some source that it can definitively only be read one way. And you didn't really answer my question. If you were to ask someone a question, and you wanted absolutely no confusion, then would you consider choosing one notation over the other? I think you're lying to yourself if you say otherwise. I don't get how "these two things are exactly the same" do not equate to "these two things are interchangeable, and therefore one is no more ambiguous than the other" in your mind. LOL, I read that and thought "What a good post, well said!" Then I reread it and realized you were saying the exact opposite of what I thought. I guess a Zeke50100 is an anti-munchmunch. And to jump into that conversation, "the same" on a semantic level is not the same as being "the same" on a syntactic level. Syntax doesn't mean a thing when it comes to ambiguity because it should be understood that both are simplified to the same level. You're suggesting that "2+1-1" would be more correct than "2-1+1" because it's syntactically more "natural" to somebody's own perception, which is what garbanzo is trying to say. Of course syntax means something when it comes to ambiguity. People who write programming language specifications have to think about syntactic ambiguity all the time. And syntactic ambiguity is by definition the ambiguities that occur before or in the process of simplification. The fact that neither "2+1-1" and "2-1+1" are neither syntactically or semantically ambiguous to most people has nothing to do with it. I agree that one is more natural than the other, but in my mind this is a third concept distinct from ambiguity or correctness (which are themselves very distinct). Anyway, I have to quit the thread now. Nice talking to you... quite fun when I'm procrastinating to meet somebody who can write well but thinks exactly the opposite to myself. Funny you should mention that, since I should probably do some work myself It's easily possible that somebody finds 2+1-1 more ambiguous to 2-1+1, which is something along the lines of what I was trying to say; however, that doesn't make one of them more ambiguous in the grand scheme of things (both being expressions of equal length and all). Anyway, with those of you saying that it would be correct in an informal setting, the problem is that this is on the internet, where an "informal" (which you should really call oral or face-to-face communication via speaking) setting is impossible in the same way sending sarcasm through text without tone is impossible. When typing, we have to assume robotic rule-following, rather than what would "normally" occur when two people communicate. Also, the reason certain languages do not accept parentheses as a function in itself is not a flaw in math, but a flaw in the language itself ^_^ this a million times. this is what i was trying to get at with my you're vs your example (maybe not the best example anyway). in an "informal" situation you understand through context but this situation gives none and therefore you should default to accepted standards. maybe there are some set of rules in upper mathematics that trumps order of operations that i don't know, though no one has brought it up. 48/2(9+3) has no multiplication operator.
In algebra, multiplication involving variables is often written as a juxtaposition (e.g. xy for x times y or 5x for five times x). This notation can also be used for quantities that are surrounded by parentheses (e.g. 5(2) or (5)(2) for five times two).
wiki says there is
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EPT
