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  #21  
Old 07 January 2013, 12:14 AM
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Quote:
Originally Posted by DaGuyWitBluGlasses View Post
E.g 3x^2 + 1/4x - 3 =0, 1/4x is a term
3x^2 + 1/4*x -3 = 0, 1/4*x is also a term
So we're still no closer to agreeing on whether 1/4x is equivelant to (1/4)x or 1/(4x)...
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  #22  
Old 07 January 2013, 01:23 AM
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I think that as you've written it, the answer is always 9 since 6/2 is a fraction which would be resolved before other calculations. but 62(1+2) is ambiguous.
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  #23  
Old 07 January 2013, 01:59 AM
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How is the latter ambiguous?

Parenthesis first gives you 6 (divided by, dunno how to do the sign) 2 * 3. Since there are only operations of equal magnitude left, you solve left to right. 6 divided by 2 is 3, and 3 * 3 is 9. That is actually less ambiguous than the other.
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  #24  
Old 07 January 2013, 02:06 AM
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It would be ambiguous if you interpret the 1+2 as inside of the divider (which is possible) making it 6 divided by 6. The bottom being calculated first of course.

That's not what is going on, but it could look that way if it was written out ambiguously which is why when they write this stuff out they make it clear where parenthesis are located so it can be calculated correct - which in this case is (I agree) 9.
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  #25  
Old 07 January 2013, 02:08 AM
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If the order of operations were always the same for all mathematics and programming languages then it would not be ambiguous. Unfortunately, they are not, as described in this wiki:
http://en.wikipedia.org/wiki/Order_of_operations
Quote:
Hence, with this interpretation we have that 1/2x is equal to (1/2)x, and not 1/(2x). However, there are examples, including in published literature, where implied multiplication is interpreted as having higher precedence than division, so that 1/2x equals 1/(2x), not (1/2)x. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,[5] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[6] Additionally, Wolfram Alpha considers that implied multiplication without parentheses precedes division, unlike explicit multiplication or implied multiplication with parentheses. 2*x/2*x and 2(x)/2(x) both yield x2, but 2x/2x yields 1.[7] The TI 89 calculator yields x2 in all three cases.
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  #26  
Old 07 January 2013, 02:20 AM
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Quote:
Originally Posted by ganzfeld View Post
If the order of operations were always the same for all mathematics and programming languages then it would not be ambiguous. Unfortunately, they are not, as described in this wiki:
That kind of takes the "universal" out of the "universal language" a bit, doesn't it?

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  #27  
Old 07 January 2013, 02:34 AM
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Quote:
Originally Posted by ganzfeld View Post
If the order of operations were always the same for all mathematics and programming languages then it would not be ambiguous. Unfortunately, they are not, as described in this wiki:
http://en.wikipedia.org/wiki/Order_of_operations
Just to be clear on the notation, since the super scripting did not carry over in the quote, a TI-89 yields x^2 in all three cases. According to the wiki article, that is.
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  #28  
Old 07 January 2013, 02:48 AM
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The binding for Wolfram Alpha described in that wiki seems to only work for variables, not for parentheses. (So Google and Wolfram Alpha both give the same answer, 9. They also return any expression in an unambiguous form before the answer, which is welcome feedback.)
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  #29  
Old 07 January 2013, 02:57 AM
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Oddly (to my mind anyway) Alpha doesn't respect the same binding for two constants separated by a space, even though it does recognize that form as an implied multiplication. So 62 4 (with a space between 2 and 4) is parsed as (6/2)*4 whereas 62x is parsed as 6/(2*x). So the question is what's 62 x (with a space between 2 and x)? Well, according to Alpha that's (6/2)*x!
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  #30  
Old 07 January 2013, 03:40 AM
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The "ambiguity" is when people imagine the portion in brackets to be part of the denominator of a fraction - if the slash is replaced by a division sign, it would be harder to envision this. I doubt that there would be any ambiguity if this is drawn by hand and the (1+2) in the OP is clearly in the numerator.
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  #31  
Old 07 January 2013, 04:09 AM
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Playing around with Word and equations. Since there were two possible ways to look at the equation I wanted to see how Word would handle them.

The first was:



Word transfers that as 6/2 (1+2) when it is put on a single line.

The next was



Word saw that as to be 6/(2(1+2)) when on a single line.

It has been many years since I had to work much with written math equations. I seem to remember it was a space between number that made a difference. 6/2 are separated by a space from (1+2) and therefore not part of the fraction. If there was no space or dot then they were together. So 2(1+2) would have been 2*(1+2) for the denominator.

Since it has been more than 20 years since I had to study and use math equations. Take no notice of my silly idea.
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  #32  
Old 07 January 2013, 04:26 AM
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If it ever comes down to a difference in whitespace you should add parentheses. The point is to communicate something effectively, not to try to trip up your audience by assuming they agree on the finer points of order of operations.
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  #33  
Old 07 January 2013, 04:54 AM
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In C, some of the order of operations that trip me up are that bitwise operators come after compares. If you do "x%4 == 0", you're checking if x is evenly divisible by 4. If you do "x&3 == 0", that looks like it should be doing the same operation except possibly more efficiently. But actually it evaluates unconditionally to 0, because it's "x&(3==0)" -> "x&0".

Quote:
Originally Posted by Hero_Mike View Post
The "ambiguity" is when people imagine the portion in brackets to be part of the denominator of a fraction - if the slash is replaced by a division sign, it would be harder to envision this. I doubt that there would be any ambiguity if this is drawn by hand and the (1+2) in the OP is clearly in the numerator.
I agree. The idea behind using the "/" symbol in place of the less standard on keyboards "" symbol is that on some level it represents the horizontal division bar, with the parts to the left on top and the parts to the right on the bottom. Thus it's easy to visualize everything to the right as being in the denominator. If they were using the "" it would be more clear that it is just an isolated operation with the normal rules of order of operations.
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  #34  
Old 07 January 2013, 05:07 AM
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And if you'll note the original post, that's the way it appears in the Facebook graphic, with the standard division symbol. It's not ambiguous at all, it's a simple test of the order of operations.

Gibbie
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  #35  
Old 07 January 2013, 05:17 AM
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Quote:
Originally Posted by Gibbie View Post
And if you'll note the original post, that's the way it appears in the Facebook graphic, with the standard division symbol. It's not ambiguous at all, it's a simple test of the order of operations.
And if you'll note Ganzfeld's post, those rules aren't quite as firmly nailed down as people seem to think. In a particular classroom, yes, you can teach a single system in a black and white way, but in the larger world it's not quite so simple.

The best thing is not to use unclear notation, and use more parentheses in situations where it's possible that it could easily be misinterpreted.
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  #36  
Old 07 January 2013, 05:26 AM
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I was addressing this part of your post:

Quote:
If they were using the "" it would be more clear that it is just an isolated operation with the normal rules of order of operations.
In the graphic that's being referenced that's how it appears. Paradiddle just didn't know how to make the notation nor share the photo. So it's not as ambiguous in the Facebook meme as is being discussed here. I agree there's better ways to write it.

Gibbie
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  #37  
Old 07 January 2013, 05:43 AM
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I did use the sign when testing this on Alpha but it makes no difference. 62x and 6/2x are both interpreted as 6/(2*x), which is correct according to many authorities, as the wiki I cited points out. You may agree with Alpha that the multiplication in 2x has a different precedence than that in 2(1+2) but it's still no less ambiguous for real communication with anything other than a compiler. That's what this question comes down to: communication between people, not rules of the game.
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  #38  
Old 07 January 2013, 06:04 AM
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I think the real lesson of this exercise isn't that people don't know the correct order of operations, nor that the order is ambiguous, but simply don't mix operators from different mathematical languages. The division operation (whether you prefer / or ) doesn't mix with the implied multiplication in 2x or 2(1+2). That's why once we get into any kind of math that uses the implied multiplication we stop using the division symbol and switch to the horizontal division bar. It's especially to avoid this kind of mess. (Also, I can't understand why anyone would want this kind of thing to be decided by a bunch of memorized rules. Communication doesn't have to be difficult.)
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  #39  
Old 07 January 2013, 01:05 PM
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the PEMDAS method is reffered to as BEDMAS around here --

Brackets
Exponents
Division
Multiplication
Addition
Subtraction
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  #40  
Old 07 January 2013, 01:34 PM
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I for one can't get any other answer than 9. How about this one: (also shared on Facebook):

4*4+4*4+4-4*4= ?
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