Diablo® III

48÷2(9+3) = ? cont.

Posts: 1,376


True. I said this already above.

False. You could create an exactly-as-powerful system of mathematics (and here I mean powerful in the technical sense--validating all the same interpreted formula etc etc) in which the order of operations was completely different. This is because the order of operations is a purely notational matter.

How certain am I of what I just said? EIGHTY FIVE PERCENT CERTAIN!


Mathematics relationships and principles aren't invented, they're discovered. You make basic tools based on real-world application (e.g. addition ; three oranges and three more oranges is six oranges; two groups of three oranges is six oranges total). And the rest of it falls in to place. That's why math is so incredible, and such a beautiful thing.

EDIT: You could change the meaning of symbols, that is true, but the basic idea that the principles of exponents have to be applied before addition and other various operational rules is non-negotiable.


In polish notation, the order of operations is always just right to left in each case.

In the expression "*^+2375" for example, the addition is resolved first, then the exponentiation, then the multiplication. (It means the same thing as what would be notated in the normal way as "((2+3)^7)*5")

Point being: order of operations depends wholly on your notational conventions. There's nothing deep or fundamental about it.
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Posts: 126
06/12/2012 02:22 PMPosted by Grimraven
I will give you guys a hint if you have abcdefg/gfedcba you can just mark all of them out and say it is one... Maybe some of you college professors have forgot about this one...


you are thinking of / as the bar accomplishing the following :

abcdefg
______
gfedcba

however, "/" does not accomplish that here
It does if you would turn your calculator onto scientific mode! There are no parentheses so all the values that are together stay in the numerator and denominator. Any addition in between the variables would change that but outside the first section of the alphabet would have no effect.
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90 Worgen Hunter
10420
Posts: 1,217


I think if I saw any student write either of those fuctions I would count off points and mock them.


They are the same.

f1(x) = (2*x*2*y*x)/4

and

f2(x) = (2*x*x*2*y)/4

which are equivalent.

It would even be fair to write it as:

f(x):(2x)(2x)(y)(1/4)

The parenthesis don't matter, and as multiplication is associative, the order in which you multiple doesn't matter. And division is equivalent to multiplying the inverse. So you can do it in any order you want.

For example:

4*4/2=8
4*(4/2)=8
(4*4)/2=8
(4/2)(4)=8.

See what we're doing?


I'm saying that anyone who would ever write anything like f(x) = 2x2y/4 needs to be verbally abused and reprimanded for being obstinate.
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Posts: 126
Whatever, I am leaving this thread because it's not possible to prove something when the disagreeing party is refusing to even listen.

When I asked to perform simple operations on calculator on 2 different equations to see that the results you will get are different I was told:

No, I just decided that (a) times (b) would be the same as (a) times (b)


You can't argue with someone who refuses to even consider different possibility because of being blinded by his own belief.

I am done.
In what universe does (a) times (b) not equal (a) times (b)?
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Posts: 1,376
Okay, show THIS problem to any practicing mathematician recognized by his peers, absent any prompting concerning order of operations, etc, and I am very certain that I know how he or she will answer.

If x = 1 and y = 2, then what quantity is represented by the following expression?

2x÷3y

Practicing mathematicians will answer 1/3.

But the 288 people will answer 4/3.

That is my prediction. Let's test it!

(I also believe the mathematicians would answer 1/3 and 288-ers would answer 4/3 were the division symbol replaced by the slashy. Half credit for me if I'm right about that at least.)
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90 Worgen Hunter
10420
Posts: 1,217
Okay, show THIS problem to any practicing mathematician recognized by his peers, absent any prompting concerning order of operations, etc, and I am very certain that I know how he or she will answer.

If x = 1 and y = 2, then what quantity is represented by the following expression?

2x÷3y

Practicing mathematicians will answer 1/3.

But the 288 people will answer 4/3.

That is my prediction. Let's test it!

(I also believe the mathematicians would answer 1/3 and 288-ers would answer 4/3 were the division symbol replaced by the slashy. Half credit for me if I'm right about that at least.)


Practicing mathematicians would call this question, and you, stupid, and say that you should feel bad
Edited by Kennyloggins#1272 on 6/12/2012 3:02 PM PDT
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Posts: 39
Okay, show THIS problem to any practicing mathematician recognized by his peers, absent any prompting concerning order of operations, etc, and I am very certain that I know how he or she will answer.

If x = 1 and y = 2, then what quantity is represented by the following expression?

2x÷3y

Practicing mathematicians will answer 1/3.

But the 288 people will answer 4/3.

That is my prediction. Let's test it!

(I also believe the mathematicians would answer 1/3 and 288-ers would answer 4/3 were the division symbol replaced by the slashy. Half credit for me if I'm right about that at least.)


Congrats Universitys agree with you and I would too
http://www.wolframalpha.com/input/?i=2x%C3%B73y%2C+x%3D1%2C+y%3D2
http://www.wolframalpha.com/input/?i=2x%2F3y%2C+x%3D1%2C+y%3D2

but they do not agree with you on the original question and neither do I.
http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29
Edited by Gilager#1578 on 6/12/2012 3:08 PM PDT
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Posts: 126
Okay, show THIS problem to any practicing mathematician recognized by his peers, absent any prompting concerning order of operations, etc, and I am very certain that I know how he or she will answer.

If x = 1 and y = 2, then what quantity is represented by the following expression?

2x÷3y

Practicing mathematicians will answer 1/3.

But the 288 people will answer 4/3.

That is my prediction. Let's test it!

(I also believe the mathematicians would answer 1/3 and 288-ers would answer 4/3 were the division symbol replaced by the slashy. Half credit for me if I'm right about that at least.)
I got 288 and I also agree that it is 1/3. Does that mean I get extra credit? What do you get for 2x/3(y)? I think that question would better suit the 288 people. I got 4/3 on that one...
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Okay, show THIS problem to any practicing mathematician recognized by his peers, absent any prompting concerning order of operations, etc, and I am very certain that I know how he or she will answer.

If x = 1 and y = 2, then what quantity is represented by the following expression?

2x÷3y

Practicing mathematicians will answer 1/3.

But the 288 people will answer 4/3.

That is my prediction. Let's test it!

(I also believe the mathematicians would answer 1/3 and 288-ers would answer 4/3 were the division symbol replaced by the slashy. Half credit for me if I'm right about that at least.)


Congrats Universitys agree with you and I would too
http://www.wolframalpha.com/input/?i=2x%C3%B73y%2C+x%3D1%2C+y%3D2
http://www.wolframalpha.com/input/?i=2x%2F3y%2C+x%3D1%2C+y%3D2

but they do not agree with you on the original question and neither do I.
http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29


*sigh* again see earlier posts about programming language and single-line prompts and input standardization and production efficiency

vs.

pure math

big difference.

Okay, show THIS problem to any practicing mathematician recognized by his peers, absent any prompting concerning order of operations, etc, and I am very certain that I know how he or she will answer.

If x = 1 and y = 2, then what quantity is represented by the following expression?

2x÷3y

Practicing mathematicians will answer 1/3.

But the 288 people will answer 4/3.

That is my prediction. Let's test it!

(I also believe the mathematicians would answer 1/3 and 288-ers would answer 4/3 were the division symbol replaced by the slashy. Half credit for me if I'm right about that at least.)


Same issue, assuming parenthesis that do not exist changes the outcome of the expression, and it is incorrect, even though W|A will think you mean (2x)/(2x) when you input 2x/2x, even though that is not technically correct. Kind of like auto-correct when you're typing in Microsoft Word. It's a courtesy afforded for simplicity's sake.

Any mathematician you pose that question to will smack you upside the head and tell you to stop trying to use purposefully ambiguous notation.

And to your whatever polish notation crap, you're just changing the meaning and order of presentation of symbols, not which mathematical principles take precedence over the other, as that is a fundamental definition of mathematics.

06/12/2012 02:52 PMPosted by Sinew
Notational conventions are directly related to order of operations, which is a fundamental principle of math. A math problem should never have a disputable answer. It can have many answers, infinite answers, but those answers are either right, or wrong. They either fulfill the constraints of the expression following the fundamental principles of math, or they don't. There is no ambiguity. This isn't about whether or not the MLA method is the correct way to site your sources. The rules of math are not open for debate. So yes, this is a discussion about the fundamental principles of math.


Correct. Where does bedmas or other OoO conventions mention vinculum (the bar separating fractions)? It doesn't directly. If you don't accept implied multiplication than you also don't accept that there is a difference between a fraction and normal division. They are the same concept.

x/y ÷ x/y

OoO left to right = x/y/x/y = x * 1/y * 1/x * 1/y = 1/y^2
Convention = x/y * y/x = xy/xy = 1

xy ÷ xy

OoO left to right = x * y ÷ x * y = y^2
standard convention = xy * 1/xy = xy/xy = 1


That's not true,

OoO left to right = [(x/y)/x]/y = 1/y * 1/y = 1/(y^2)

And your second example,

xy ÷ xy

OoO left to right = [(x*y)/x]*y=y^2 which is correct.

I think you're very confused.

Did I miss any other fail out there?
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f1(x) = 2x2y/4x
f1(x) = 2x/1 * 2y/1 * 1/4x
= [2(x*y)]/(4x)
=(2/4)[(x*y)/x]
=(2/4)(y)

f1(x) = (2*x*2*y*x)/4


what is that?
= (4x^2(y))/4 wat?

and

f2(x) = 2x/4x2y
f2(x) = 2x/1 * 1/4x * 1/2y
= [(2)(x)]/[(2)(2x*y)]
= x/(2x*y)
=1/(x*y)


f2(x) = (2*x*x*2*y)/4


= (4x^2(y))/4 = x^2(y)

???

Where did you learn equivalency goodsir. I wish to avoid it.


Uhhh.... you said anyone that thought they were equivalent is probably in the "288" camp. You just proved they are equivalent (both equaling (x^2)*y), and yet you're championing the "2" camp. You, good sir, have confused yourself.
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That's not true,

OoO left to right = [(x/y)/x]/y = 1/y * 1/y = 1/(y^2)

And your second example,

xy ÷ xy

OoO left to right = [(x*y)/x]*y=y^2 which is correct.

I think you're very confused.

Did I miss any other fail out there?


Might want to check my answer for left to right before you derp about other people.


Ah I missed that. Yeah, OoO is standard convention, so now you're just... I dunno what you're doing, making up your own conventions?

OoO is standard mathematical convention, your "standard convention" is exceptional programming convention for single-line entry of complicated expressions, which is in no way standard. What are you getting at here?
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You nay-sayers are literally just taking certain lines out of context and jumping all over it like a drowning man on a life raft, because your argument is literally drowning in a sea of logic and proofs.

Can you present definitive evidence to the contrary, or will you continue to grasp at straws?
Edited by Mayde#1748 on 6/12/2012 3:34 PM PDT
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Posts: 126
I would expect someone that wrote a/b(x) on paper on the same line to mean that a/b is a fraction that is multiplied by (x). I would also expect someone that wrote a/bx to mean that (a) was divided by (b) and (x) after they where multiplied together. (also as written on a single line on paper) I would also think that someone that wrote (a)/(bx) had way to much time on their hands in order to write the extra parathenses and they could leave them out to prevent having to sharpen their pencil as much. Someone that wrote a/(bx) might be a little confused about where they should add parentheses. I would expect all these things because that is the way that it is done. You can try to change it but people will just think that you don't know the first thing about how to do math. Myself included.

Parentheses means multiplication, hope that helps.
Edited by Windscar#1524 on 6/12/2012 3:47 PM PDT
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06/12/2012 03:37 PMPosted by Windscar
I would expect someone that wrote a/b(x) on paper on the same line to mean that a/b is a fraction that is multiplied by (x). I would also expect someone that wrote a/bx to mean that (a) was divided by (b) and (x) after they where multiplied together. (also as written on a single line on paper) I would also think that someone that wrote (a)/(bx) had way to much time on their hands in order to write the extra parathenses and they could leave them out to prevent having to sharpen their pencil as much. Someone that wrote a/(bx) might be a little confused about where they should add parentheses. I would expect all these things because that is the way that it is done. You can try to change it but people will just think that you don't know the first thing about how to do math. Myself included.


The last example you gave, of a/(bx), it the only example of an efficiently punctuated non-ambiguous equation.... And by your following caveat I would assume that you would fall into the "don't know how to do math" area...

Your first example is correct, although the extra parenthetic notation is extraneous;

Your second example is just wrong;

Your third example is technically correct, but uses extraneous parenthetic notation and therefore is inefficient;

Your last example is the only truly correct one.

EDIT: And here I am assuming all this is common knowledge; I didn't realize people were this bad at math. No wonder I get paid so much.
Edited by Mayde#1748 on 6/12/2012 3:51 PM PDT
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Posts: 1,376
06/12/2012 03:22 PMPosted by Mayde
And to your whatever polish notation crap,


Uh hmm.... didn't you say you teach math?

Interesting.
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06/12/2012 03:54 PMPosted by Speusippus
And to your whatever polish notation crap,


Uh hmm.... didn't you say you teach math?

Interesting.


No, I don't; I'm an engineer, not a math teacher. Although I have a degree in Math and Structural Engineering.

And I was being dismissive of your erroneous comparison, which failed to address the fact that mathematical principles have a definitive order of applicability regardless of particular arrangement or standard of notation, which is what you were trying to prove. Exponents still take precedence over addition, no matter how you denote those two operations.

Again, as I said before:

You nay-sayers are literally just taking certain lines out of context and jumping all over it like a drowning man on a life raft, because your argument is literally drowning in a sea of logic and proofs.

Can you present definitive evidence to the contrary, or will you continue to grasp at straws?
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Posts: 1,376
Okay, show THIS problem to any practicing mathematician recognized by his peers, absent any prompting concerning order of operations, etc, and I am very certain that I know how he or she will answer.

If x = 1 and y = 2, then what quantity is represented by the following expression?

2x÷3y

Practicing mathematicians will answer 1/3.

But the 288 people will answer 4/3.

That is my prediction. Let's test it!

(I also believe the mathematicians would answer 1/3 and 288-ers would answer 4/3 were the division symbol replaced by the slashy. Half credit for me if I'm right about that at least.)


Congrats Universitys agree with you and I would too
http://www.wolframalpha.com/input/?i=2x%C3%B73y%2C+x%3D1%2C+y%3D2
http://www.wolframalpha.com/input/?i=2x%2F3y%2C+x%3D1%2C+y%3D2

but they do not agree with you on the original question and neither do I.
http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29


I can't see how it's possible for a person to agree in one case and not the other, unless they are switching between notational conventions.
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