Diablo® III

48÷2(9+3) = ? cont.

08/02/2012 01:32 PMPosted by Saigyouji
Alternatively, it's proof that you should use bracketing instead of relying on conventions about ordering.


Too much bracketing can make lines quite unreadable. If you are clear on what convention you use it's not a problem. In any case you need conventions to say how a line should be read. The very fact of doing operations inside the brackets first is a convention after all.

Binary operations, as well-defined functions, have a unique, unambiguous image point corresponding to any pair of numbers. As long as you use brackets, it's always explicit which two numbers are in that pair.


Would you recommand to use brackets to do an operation like : x*y*z ?
I understand what you say, and agree, but in some cases getting rid of unnecessary brackets isn't that bad.
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The very fact of doing operations inside the brackets first is a convention after all.


Not really. Given (3 - 3) / 2, the term "3) / 2" isn't even well formed. I wouldn't really call that a convention o_O. It's not even that you're doing the thing in the brackets first, it's that you're treating it as a single object. One could essentially "do the division first" by distributing the 2 and getting (3/2 - 3/2) before doing any subtraction.

Would you recommand to use brackets to do an operation like : x*y*z ?


The point of brackets is to remove ambiguity. Assuming * is associative, bracketing is superfluous since the term can be defined by x*y*z = (x*y)*z = x*(y*z)
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Not really. Given (3 - 3) / 2, the term "3) / 2" isn't even well formed.


And how can you tell that a line is well formed or not? "(3 - 3) / 2" is a succession of mathematical symbols, it has no meaning unless you give it one.

With proper conventions you can give a meaning to "3) / 2" so it would be well formed. it's not very interesting tho ^^.

Saying that something inside a bracket should be treated as a single object is a convention. Everyone uses this convention, but it's still is one.

The point of brackets is to remove ambiguity. Assuming * is associative, bracketing is superfluous since the term can be defined by x*y*z = (x*y)*z = x*(y*z)


So is the point of conventions. Assuming that operations with same level of priority should be done left to right there is absolutely no abiguity in the term "x÷y*z". Hence bracketing become superfluous.
Edited by Cognus#2405 on 8/2/2012 8:58 PM PDT
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And how can you tell that a line is well formed or not? "(3 - 3) / 2" is a succession of mathematical symbols, it has no meaning unless you give it one.

With proper conventions you can give a meaning to "3) / 2" so it would be well formed. it's not very interesting tho ^^.

Saying that something inside a bracket should be treated as a single object is a convention. Everyone uses this convention, but it's still is one.


Brackets are built into the language, as is the definition of a 'term'. It's no more of a convention than the decision to treat the plus sign as addition. BEDMAS, however, is not built into the language.

So is the point of conventions. Assuming that operations with same level of priority should be done left to right there is absolutely no abiguity in the term "x÷y*z". Hence bracketing become superfluous.


Right, but given that BEDMAS isn't built into the language itself, adding implied conventions on top of it can result in confusion and inconsistency. As an example, type 2x/2x into Wolfram Alpha. According to BEDMAS it should be ((2*x)/2)*x = x^2, right? Yet Wolfram Alpha gives 1. It treats it as (2*x)/(2*x), because no one writes 2x/2x with the former interpretation in mind.
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08/03/2012 04:47 AMPosted by Saigyouji
It's no more of a convention than the decision to treat the plus sign as addition.


Without aggreeing on it's meaning the plus sign is nothing more than a cross. Treating it as addition is a convention.
We could say otherwise, for example in boolean algerba it's current to use the sign + to mean "or".

because no one writes 2x/2x with the former interpretation in mind.


And we completely agree that no one should write such a line in any case whatever he has in mind ^^.
Seriously writing division in line and not using fractional notation is a bad idea.

I just tried to ask wolfram alpha about 2x/2*x and in that case it answer x². It uses the third convention I exprimed in post #417, it doesn't count 2x as a multiplication but as a single object.
It's very common, one does think that a non written multiplication is of higher priority than a written one.

Right, but given that BEDMAS isn't built into the language itself


And how do you build the language ?
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Without aggreeing on it's meaning the plus sign is nothing more than a cross. Treating it as addition is a convention.
We could say otherwise, for example in boolean algerba it's current to use the sign + to mean "or".


The point is that not all conventions are the same. Without a common understanding of what the symbols mean, communication isn't even possible. An implicit convention for unambiguously understanding lazy arithmetic writing that goes against common sense at times (like when implicit multiplication is involved) is not like the convention that we understand + to mean addition rather than flying monkey olympics.

Seriously writing division in line and not using fractional notation is a bad idea.


Yet it's done all the time and is completely unambiguous and easy to understand with proper use of bracketing. (2x^2 + 3x - 9) / (ix^2 - 3) is unproblematic.

I just tried to ask wolfram alpha about 2x/2*x and in that case it answer x². It uses the third convention I exprimed in post #417, it doesn't count 2x as a multiplication but as a single object.
It's very common, one does think that a non written multiplication is of higher priority than a written one.


So BEDMAS is wrong? It's actually BEIDMAS, with the 'I' for 'implicit'?

All the more reason to scrap unnecessary conventions.

And how do you build the language ?


That would take a while to explain, though there's nothing complicated (or controversial) about it:

http://en.wikipedia.org/wiki/First-order_logic#Syntax
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Without a common understanding of what the symbols mean, communication isn't even possible.


A common understanding is a convention. Without conventions communication isn't even possible.
We agree on the meaning of things. We agree to all speak english here, if we didn't agree on that, communication would be quite hard. But we could also have chosen french or even esperanto as long as everyone speaks the same language.

Yet it's done all the time and is completely unambiguous and easy to understand with proper use of bracketing. (2x^2 + 3x - 9) / (ix^2 - 3) is unproblematic.


Is that so? "2x^2" means "(2x)^2" or "2(x^2)"? Of course I know it's the second one, we all know the convention perfectly well and therefore there's no ambiguity.
The problem with a line like "2x/2x" is that no one knows the convention. You say that a convention is unnecessary if we use brackets and I say that brackets are unnecessary with proper convention.

Couldn't we just agree that we need either one?

So BEDMAS is wrong? It's actually BEIDMAS, with the 'I' for 'implicit'?


So says wolfram alpha apparently. It doesn't mean I agree with it. For me every kind of multiplication has same level of priority as division. Without bracketing I go left to right, therefore 2x/2x = x².

If I write something like that just for me or for someone I know uses the same convention I use, there is no problem.
If I write this for someone else, I would be careful. I may use brackets because I know the person I write my line for uses the same convention for the meaning of brackets I use (almost everyone does ^^). But I may also write down my convention. In that very case it's stupid, but there are lots of cases where writing down the convention you use in a math exam is no waste of time.


That would take a while to explain, though there's nothing complicated (or controversial) about it:

http://en.wikipedia.org/wiki/First-order_logic#Syntax


I know how to construct first-order logic, but you're going too far above the question. I was just asking how you build the language you need to do elementary maths, nothing more than division. At that point you can assume logic.
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Is that so? "2x^2" means "(2x)^2" or "2(x^2)"? Of course I know it's the second one, we all know the convention perfectly well and therefore there's no ambiguity. The problem with a line like "2x/2x" is that no one knows the convention. You say that a convention is unnecessary if we use brackets and I say that brackets are unnecessary with proper convention.

Couldn't we just agree that we need either one?


Everyone will correctly interpret 2x/(2x). There will be disagreements over the interpretation of 2x/2x. The problem with conventions like BEDMAS is that a convention only works insofar as it's universally known and accepted. Furthermore, as this particular example illustrates, newer conventions that arise out of popular use (like treating implied multiplication as involving single objects) will cause new ambiguities, but only without proper bracketing.
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85 Blood Elf Priest
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Posts: 69
Rewrite the equation so everyone knows what it is saying: 48/1 x 1/2 x (9+3)/1 then solve...the only thing the parenthesis do is cause you to add 9+3 first...then do all the multiplication. Division is multiplication by the reciprocal, so it has the same order of operation. If you rewrite the equation properly, as I did, the answer is 288, no other possibility. The parenthesis do not mean to distribute the 2x rather to do the addition first.
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85 Blood Elf Priest
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Posts: 69
Juggernaut

What is happening here is that people are not following the golden rules of Math!!!

1) There is only one correct answer per question. Implying has no place in Math


Is that so....what is the square root of 4? It can be 2 or -2...two answers
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85 Blood Elf Priest
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Posts: 69
Speusippus

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.

Since you are using variables, the 2 and 3 are coefficients, and part of the number, so 1/3 is correct, in the original question, there were no variables, so all numbers are equal, and you go by operation order, and get 288...its that simple. People are confusing variable and coefficients with numbers, there is a big difference.

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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85 Blood Elf Priest
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Posts: 69
Kennyloggins
85 Worgen Hunter
Midwinter
6235


The 288 camp are seriously daft.

sin2x != 2sinx

Actually, untrue...sin of 30 is .5 sin of 60 is .8660269....not 1

Actually sin(2x) = 2sin(x) whenever x = nπ where n is an integer
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Juggernaut

What is happening here is that people are not following the golden rules of Math!!!

1) There is only one correct answer per question. Implying has no place in Math


Is that so....what is the square root of 4? It can be 2 or -2...two answers


Yeah... I can't remembe if I was drunk while I wrote that or if I was just making up a bunch of random rules on the spot.

Good catch, I wasn't thinking of square roots at the time.
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There are clearly two answers to this equation

288 using Order of Operations, Excel, and/or common sense.

2 using "what passes for an education these days in the public school system."
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