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On July 29 2012 16:35 TheRabidDeer wrote:Show nested quote +On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:On July 29 2012 15:52 TheRabidDeer wrote:On July 29 2012 15:44 paralleluniverse wrote:
[quote]
These are the type of showy and pointless trick questions that I absolutely despise.
So what does it prove? That people have failed to learn the order of operations? So what?
The order of operation is simply a convention. It's not a law of the universe nor a theorem of mathematics.
It's not actually wrong to interpret 1+1*0 as 0 instead of the usual convention that says it's equal to 1.
Moreover, in basically all scientific discourse or displaying of equations in real mathematics, grouping symbols like brackets are used. So not knowing the order of operations is not a big deal even if you do math. It proves that a lot of people have very little grasp on following a VERY simple logical procedure. I glanced at the comments and TONS of them said something along the lines of, "anything multiplied by 0 is 0 so it is 0". And we group things to make them easier to read, but the conventions still follow. I mean, its not even close to a trick question. .99999_ = 1 is a trick question. What does it say when close to 60% of the population cant follow PEMDAS? EDIT: Yes, we do use parenthesis to make it easier to read, but that doesnt make it any better. It is NOT a logical procedure. It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go?
Furthermore,
x * 4 + 8 * 2 = 10
Proper order of operations will make 4x+16=10, and x=-3/2
Without PEMDAS, you could end up with x * 12 * 2 = 10, or 24x = 10 and x=5/6.
With just 2 numbers like 2x+2=0 the number of actions you can actually take is very limited, but with 4 numbers like above you already get into more complicated scenarios without predetermined order.
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Not one person has given a compelling reason how making algebra mandatory improves critical thinking skills. All of you supporting and condeming it are missing the basic problem. The entire world teaches algebra to their students but nowhere has it ever been shown to improve the quality of the people who learn it. All of you talking about tools and learning skills and resonating knowledge do not one shred of evidence for your position beyond asserting it as fact repeatedly. Show me any data than doesn't even imply, just correlate thats all I ask, any data that would link studying algebra to improving learning skills, because if it doesn't do that, we are teaching an irrelevant subject to millions of people.
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On July 29 2012 16:30 paralleluniverse wrote:Show nested quote +On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:On July 29 2012 15:52 TheRabidDeer wrote:On July 29 2012 15:44 paralleluniverse wrote:On July 29 2012 15:37 TheRabidDeer wrote:I saw this on my facebook recently: ![[image loading]](http://i.imgur.com/CKKQl.jpg) This is indicative of how bad the education system is for americans (in terms of math). Personally, I never had too big of a problem with math... and I actually love algebra because of how simple it is and how much application I can get out of it on a day to day basis. I can use algebra for games (especially RPG's), figuring out tips, and all kinds of other stuff. I am curious though, what is it with algebra that people dont get? It is a simple set of rules that you follow, and thats it. You can even guess and check a lot of things if you have the time. These are the type of showy and pointless trick questions that I absolutely despise. So what does it prove? That people have failed to learn the order of operations? So what? The order of operation is simply a convention. It's not a law of the universe nor a theorem of mathematics. It's not actually wrong to interpret 1+1*0 as 0 instead of the usual convention that says it's equal to 1. Moreover, in basically all scientific discourse or displaying of equations in real mathematics, grouping symbols like brackets are used. So not knowing the order of operations is not a big deal even if you do math. It proves that a lot of people have very little grasp on following a VERY simple logical procedure. I glanced at the comments and TONS of them said something along the lines of, "anything multiplied by 0 is 0 so it is 0". And we group things to make them easier to read, but the conventions still follow. I mean, its not even close to a trick question. .99999_ = 1 is a trick question. What does it say when close to 60% of the population cant follow PEMDAS? EDIT: Yes, we do use parenthesis to make it easier to read, but that doesnt make it any better. It is NOT a logical procedure. It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0. You can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. You can even apply exp to both sides to get [exp(x+1)]^2=1, so that exp(x+1)=1, and then log both sides to get x+1=0, then x=-1.
Following the proper mathematical convention is fundamental to maths. If you can't do it, you get the answer wrong. As such, I don't have any problem with the initial trick problem in this discussion.
Mathematical equations have to be followed logically and in the correct convention to make sense. Equations are not and should not be open to interpretation.
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On July 29 2012 16:37 Mallard86 wrote:Show nested quote +On July 29 2012 16:31 TheRabidDeer wrote:On July 29 2012 16:28 Mallard86 wrote:On July 29 2012 16:26 TheRabidDeer wrote:On July 29 2012 16:23 paralleluniverse wrote:On July 29 2012 16:16 r.Evo wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:On July 29 2012 15:52 TheRabidDeer wrote:
[quote]
It proves that a lot of people have very little grasp on following a VERY simple logical procedure. I glanced at the comments and TONS of them said something along the lines of, "anything multiplied by 0 is 0 so it is 0". And we group things to make them easier to read, but the conventions still follow.
I mean, its not even close to a trick question. .99999_ = 1 is a trick question.
What does it say when close to 60% of the population cant follow PEMDAS?
EDIT: Yes, we do use parenthesis to make it easier to read, but that doesnt make it any better. It is NOT a logical procedure. It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon.
There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Actually I think you're wrong. If I can believe one of my better math teachers t he reason for multiplication first is that a multiplication is just short for multiple additions. e.g. 3 x 7 + 4 x 5 has to give the same result as 7+7+7+5+5+5+5 or 3+3+3+3+3+3+3 and 4+4+4+4+4. The result in both of those additions is 41. Getting this result with using multiplicatives instead of multiple additives is ONLY possible if you deal with the multiplications first. PS: FUCK YES I LEARNED SOMETHING IN MATH. My teacher would be proud of me. PPS: The feeling of being a complete math-smartass is fucking awesome. Why did I never think of that during school? Now you're just stacking convention on top of convention. Why should 3 x 7 + 4 x 5 mean 7+7+7+5+5+5+5 instead of [(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]? The idea that multiplication is repeated addition is something that is taught in primary school, but it's not generally true, how is pi*e, the sum of pi, repeated e times? Again, you only know it is that order because youve learned it. Somebody new might try to pair it up as 3 x (7 + 4) x 5. They dont know the brackets arent supposed to go there. They just see some numbers and they know they need brackets somewhere. Also, pi * e is the sum of pi repeated e times, it is just strange because you have awkward numbers. Now you are arguing against yourself. If it has to be explained then it is not naturally logical. log·ic [loj-ik] Show IPA noun 1. the science that investigates the principles governing correct or reliable inference. That is to say you follow a known pattern. I dont know if I can think of anything off the top of my head that is "naturally logical". Maybe music... MAYBE... though most music has a learned structure too. Westerners read from left to right and reading is usually something learned well before algebra. PEMBAS is not a naturally logical conclusion from the perspective of the western reader because it does not always follow the previously set standard of left to right.
Westerners read left to right top to bottom, but many forms of music have you read 2 bars at the same time. Music is not natural.
Also, PEMDAS exists because math generally requires you to use logic, not "natural logic". Whatever that may actually mean.
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On July 29 2012 16:35 TheRabidDeer wrote:Show nested quote +On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:On July 29 2012 15:52 TheRabidDeer wrote:On July 29 2012 15:44 paralleluniverse wrote:
[quote]
These are the type of showy and pointless trick questions that I absolutely despise.
So what does it prove? That people have failed to learn the order of operations? So what?
The order of operation is simply a convention. It's not a law of the universe nor a theorem of mathematics.
It's not actually wrong to interpret 1+1*0 as 0 instead of the usual convention that says it's equal to 1.
Moreover, in basically all scientific discourse or displaying of equations in real mathematics, grouping symbols like brackets are used. So not knowing the order of operations is not a big deal even if you do math. It proves that a lot of people have very little grasp on following a VERY simple logical procedure. I glanced at the comments and TONS of them said something along the lines of, "anything multiplied by 0 is 0 so it is 0". And we group things to make them easier to read, but the conventions still follow. I mean, its not even close to a trick question. .99999_ = 1 is a trick question. What does it say when close to 60% of the population cant follow PEMDAS? EDIT: Yes, we do use parenthesis to make it easier to read, but that doesnt make it any better. It is NOT a logical procedure. It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go?
Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts.
The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French.
Then the convention I stated, putting x=1 gives 4, under the usual convention it's 3, but that's because 2 different concepts are written. The concept that my example expresses is 2(x+1), so (2x)+1 would be an incorrect translation of the concept -- a misreading.
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The simple answer is to track people by scholastic ability like the rest of the civilized world.
This coming fall, my college will have more sections of arithmetic than of Calc 1 and all subsequent math combined. At a glance, it seems like little more than a Pell Grant farm.
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On July 29 2012 16:41 paralleluniverse wrote:Show nested quote +On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:On July 29 2012 15:52 TheRabidDeer wrote:
[quote]
It proves that a lot of people have very little grasp on following a VERY simple logical procedure. I glanced at the comments and TONS of them said something along the lines of, "anything multiplied by 0 is 0 so it is 0". And we group things to make them easier to read, but the conventions still follow.
I mean, its not even close to a trick question. .99999_ = 1 is a trick question.
What does it say when close to 60% of the population cant follow PEMDAS?
EDIT: Yes, we do use parenthesis to make it easier to read, but that doesnt make it any better. It is NOT a logical procedure. It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts. The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French.
Are you saying there are different accepted forms of mathematical expression, like different languages?
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On July 29 2012 16:41 paralleluniverse wrote:Show nested quote +On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:On July 29 2012 15:52 TheRabidDeer wrote:
[quote]
It proves that a lot of people have very little grasp on following a VERY simple logical procedure. I glanced at the comments and TONS of them said something along the lines of, "anything multiplied by 0 is 0 so it is 0". And we group things to make them easier to read, but the conventions still follow.
I mean, its not even close to a trick question. .99999_ = 1 is a trick question.
What does it say when close to 60% of the population cant follow PEMDAS?
EDIT: Yes, we do use parenthesis to make it easier to read, but that doesnt make it any better. It is NOT a logical procedure. It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts. The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French.
Yes, everyone agrees we do brackets first. Where are the brackets coming from? Who decides where they go? A person is trying to solve this simple problem (or worse still, trying to come up with an equation of their own), but the brackets arent there. What do they do?
2(1 + 1) = 4 is entirely different from 2(1) + 1 = 3, and yet 2x + 1 = 0 could represent either in your world.
Also, 9^2 + 3^2 gets you a different answer from (9+3)*(9+3). One gives you 144 the other gets you 90. That is not purely convention.
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On July 29 2012 16:43 thesideshow wrote:Show nested quote +On July 29 2012 16:41 paralleluniverse wrote:On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:
[quote]
It is NOT a logical procedure.
It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts. The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French. Are you saying there are different accepted forms of mathematical expression, like different languages?
Usually not, but there are.
For example, the inner product <.,.> is linear in the first slot for mathematicians, but linear in the second slot for physicists.
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On July 29 2012 16:40 TheRabidDeer wrote:Show nested quote +On July 29 2012 16:37 Mallard86 wrote:On July 29 2012 16:31 TheRabidDeer wrote:On July 29 2012 16:28 Mallard86 wrote:On July 29 2012 16:26 TheRabidDeer wrote:On July 29 2012 16:23 paralleluniverse wrote:On July 29 2012 16:16 r.Evo wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:
[quote]
It is NOT a logical procedure.
It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon.
There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Actually I think you're wrong. If I can believe one of my better math teachers t he reason for multiplication first is that a multiplication is just short for multiple additions. e.g. 3 x 7 + 4 x 5 has to give the same result as 7+7+7+5+5+5+5 or 3+3+3+3+3+3+3 and 4+4+4+4+4. The result in both of those additions is 41. Getting this result with using multiplicatives instead of multiple additives is ONLY possible if you deal with the multiplications first. PS: FUCK YES I LEARNED SOMETHING IN MATH. My teacher would be proud of me. PPS: The feeling of being a complete math-smartass is fucking awesome. Why did I never think of that during school? Now you're just stacking convention on top of convention. Why should 3 x 7 + 4 x 5 mean 7+7+7+5+5+5+5 instead of [(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]? The idea that multiplication is repeated addition is something that is taught in primary school, but it's not generally true, how is pi*e, the sum of pi, repeated e times? Again, you only know it is that order because youve learned it. Somebody new might try to pair it up as 3 x (7 + 4) x 5. They dont know the brackets arent supposed to go there. They just see some numbers and they know they need brackets somewhere. Also, pi * e is the sum of pi repeated e times, it is just strange because you have awkward numbers. Now you are arguing against yourself. If it has to be explained then it is not naturally logical. log·ic [loj-ik] Show IPA noun 1. the science that investigates the principles governing correct or reliable inference. That is to say you follow a known pattern. I dont know if I can think of anything off the top of my head that is "naturally logical". Maybe music... MAYBE... though most music has a learned structure too. Westerners read from left to right and reading is usually something learned well before algebra. PEMBAS is not a naturally logical conclusion from the perspective of the western reader because it does not always follow the previously set standard of left to right. Westerners read left to right top to bottom, but many forms of music have you read 2 bars at the same time. Music is not natural. Also, PEMDAS exists because math generally requires you to use logic, not "natural logic". Whatever that may actually mean.
Why dont you actually read your own quote?
You are criticizing the population for not being able to follow a simple logical procedure yet it is not a simple logical procedure if it has not been taught or it has been taught and the knowledge was not retained.
If you want to criticize the population for ignorance then go ahead but dont claim the population is stupid for not being able to follow a simple set of rules when they dont know the rules.
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On July 29 2012 16:45 TheRabidDeer wrote:Show nested quote +On July 29 2012 16:41 paralleluniverse wrote:On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:
[quote]
It is NOT a logical procedure.
It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts. The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French. Yes, everyone agrees we do brackets first. Where are the brackets coming from? Who decides where they go? A person is trying to solve this simple problem (or worse still, trying to come up with an equation of their own), but the brackets arent there. What do they do? 2(1 + 1) = 4 is entirely different from 2(1) + 1 = 3, and yet 2x + 1 = 0 could represent either in your world. Also, 9^2 + 3^2 gets you a different answer from (9+3)*(9+3). One gives you 144 the other gets you 90. That is not purely convention.
...Different because you're expressing different concepts.
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United States10328 Posts
Wow, this is getting pretty silly...
I think everyone agrees that PEMDAS is a useful convention.
What paralleluniverse is trying to say is that the accepted order-of-operations is a convention that is not inherent to our understanding of math, but is rather a tool to convey mathematical expressions precisely. But nothing's inherently worse about evaluating expression written in Polish notation or expressions that are meant to be evaluated left-to-right---something which programmers might do, though it may look different:
x = 0
x += 2
x *= 4
etc.
Using PEMDAS to evaluate algebraic expressions is just as important as using base 10 numbers. That is, it makes communication much more convenient (and, therefore, educated [in the Western sense] people should know how to use it), so it is indeed sad that so many people got that wrong.
But an actual mathematician is concerned about maps between objects and universal properties rather than explicit constructions (that is, how an object behaves, not how it's written; the written convention is merely for communication's sake), so he reasonably would not see a test of "knowledge of convention" as a test of mathematical aptitude.
(Edit: if you're a programmer, the last paragraph has a good analogue: you don't care how a library function is implemented [what variable names it uses, if the programmer puts curly braces on their own lines or not, etc.], but rather about the interface it exposes.)
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On July 29 2012 16:40 UrsusRex wrote:
Not one person has given a compelling reason how making algebra mandatory improves critical thinking skills. All of you supporting and condeming it are missing the basic problem. The entire world teaches algebra to their students but nowhere has it ever been shown to improve the quality of the people who learn it. All of you talking about tools and learning skills and resonating knowledge do not one shred of evidence for your position beyond asserting it as fact repeatedly. Show me any data than doesn't even imply, just correlate thats all I ask, any data that would link studying algebra to improving learning skills, because if it doesn't do that, we are teaching an irrelevant subject to millions of people.
algebra is like artificial problems, follow a set of rules to figure out an answer. the set of rules require you to focus your thought and think of a way to find the answer. that seems like a pretty transferable skill to me.
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On July 29 2012 16:41 paralleluniverse wrote:Show nested quote +On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:On July 29 2012 15:52 TheRabidDeer wrote:
[quote]
It proves that a lot of people have very little grasp on following a VERY simple logical procedure. I glanced at the comments and TONS of them said something along the lines of, "anything multiplied by 0 is 0 so it is 0". And we group things to make them easier to read, but the conventions still follow.
I mean, its not even close to a trick question. .99999_ = 1 is a trick question.
What does it say when close to 60% of the population cant follow PEMDAS?
EDIT: Yes, we do use parenthesis to make it easier to read, but that doesnt make it any better. It is NOT a logical procedure. It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts. The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French. Then the convention I stated, putting x=1 gives 4, under the usual convention it's 3, but that's because 2 different concepts are written. The concept that my example expresses is 2(x+1), so (2x)+1 would be an incorrect translation of the concept -- a misreading.
Why are you arguing about notation?
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On July 29 2012 16:47 Mallard86 wrote:Show nested quote +On July 29 2012 16:40 TheRabidDeer wrote:On July 29 2012 16:37 Mallard86 wrote:On July 29 2012 16:31 TheRabidDeer wrote:On July 29 2012 16:28 Mallard86 wrote:On July 29 2012 16:26 TheRabidDeer wrote:On July 29 2012 16:23 paralleluniverse wrote:On July 29 2012 16:16 r.Evo wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:
[quote]
position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position)
Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon.
There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Actually I think you're wrong. If I can believe one of my better math teachers t he reason for multiplication first is that a multiplication is just short for multiple additions. e.g. 3 x 7 + 4 x 5 has to give the same result as 7+7+7+5+5+5+5 or 3+3+3+3+3+3+3 and 4+4+4+4+4. The result in both of those additions is 41. Getting this result with using multiplicatives instead of multiple additives is ONLY possible if you deal with the multiplications first. PS: FUCK YES I LEARNED SOMETHING IN MATH. My teacher would be proud of me. PPS: The feeling of being a complete math-smartass is fucking awesome. Why did I never think of that during school? Now you're just stacking convention on top of convention. Why should 3 x 7 + 4 x 5 mean 7+7+7+5+5+5+5 instead of [(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]? The idea that multiplication is repeated addition is something that is taught in primary school, but it's not generally true, how is pi*e, the sum of pi, repeated e times? Again, you only know it is that order because youve learned it. Somebody new might try to pair it up as 3 x (7 + 4) x 5. They dont know the brackets arent supposed to go there. They just see some numbers and they know they need brackets somewhere. Also, pi * e is the sum of pi repeated e times, it is just strange because you have awkward numbers. Now you are arguing against yourself. If it has to be explained then it is not naturally logical. log·ic [loj-ik] Show IPA noun 1. the science that investigates the principles governing correct or reliable inference. That is to say you follow a known pattern. I dont know if I can think of anything off the top of my head that is "naturally logical". Maybe music... MAYBE... though most music has a learned structure too. Westerners read from left to right and reading is usually something learned well before algebra. PEMBAS is not a naturally logical conclusion from the perspective of the western reader because it does not always follow the previously set standard of left to right. Westerners read left to right top to bottom, but many forms of music have you read 2 bars at the same time. Music is not natural. Also, PEMDAS exists because math generally requires you to use logic, not "natural logic". Whatever that may actually mean. Why dont you actually read your own quote? You are criticizing the population for not being able to follow a simple logical procedure yet it is not a simple logical procedure if it has not been taught or it has been taught and the knowledge was not retained. If you want to criticize the population for ignorance then go ahead but dont claim the population is stupid for not being able to follow a simple set of rules when they dont know the rules.
PEMDAS is taught in 4th grade (or earlier) and is used for every single bit of math beyond 4th grade. If you cant retain the knowledge of the foundations in math by the time you are in high school, that is a failure of teaching and learning. If I stopped learning english rules in the 4th grade, that would be a damned shame.
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On July 29 2012 16:36 RageBot wrote:
Algebra isn't neccessary in itself, but as a roadblock for dumb (or "not so smart herp derp") people.
Honestly, if someone can't pass highschool algebra, he just isn't smart.
And also, they talk about lowering the demands for the SAT? This is really fucking stupid.
Some people are bad in things, some people are good in things, we are not equal, life has winners and losers, deal with it.
You haven't said why people should be forced to learn algebra when they're not going to use it, and they want to be a mathematician or engineer or whatever.
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On July 29 2012 16:46 paralleluniverse wrote:Show nested quote +On July 29 2012 16:43 thesideshow wrote:On July 29 2012 16:41 paralleluniverse wrote:On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:
[quote]
position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position)
Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts. The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French. Are you saying there are different accepted forms of mathematical expression, like different languages? Usually not, but there are. For example, the inner product <.,.> is linear in the first slot for mathematicians, but linear in the second slot for physicists.
is there any other way to interpret 5 + 5 + 5 + 5 - 5 + 5 - 5 + 5 * 0 (or whatever the original question was), that is widely accepted?
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OP would be better if it had a poll. That way we could easily see the majority agree that the author of the article is an imbecile.
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On July 29 2012 16:49 sOda~ wrote:Show nested quote +On July 29 2012 16:41 paralleluniverse wrote:On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:On July 29 2012 15:55 paralleluniverse wrote:
[quote]
It is NOT a logical procedure.
It's an arbitrary man-made convention. position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position) Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts. The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French. Then the convention I stated, putting x=1 gives 4, under the usual convention it's 3, but that's because 2 different concepts are written. The concept that my example expresses is 2(x+1), so (2x)+1 would be an incorrect translation of the concept -- a misreading. Why are you arguing about notation?
Because some people think they are sooooo smart because they memorized that the usual convention is to do multiplication before addition, and that our educational system has failed because most people have failed to remember this arbitrary convention.
It reflects the sad state of education that people are obsessively fixated on written notation to prove that people are stupid, instead of the understanding of actual mathematical concepts.
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On July 29 2012 16:46 paralleluniverse wrote:
For example, the inner product <.,.> is linear in the first slot for mathematicians, but linear in the second slot for physicists.
An inner product is bilinear you noob!
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EPT
