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On April 08 2011 17:59 MasterOfChaos wrote:Show nested quote +On April 08 2011 17:53 sleepingdog wrote:On April 08 2011 17:39 MasterOfChaos wrote:
Is there any official specification of mathematical notation? This is an argument about the grammar of mathematical notation. "What operator precedence does an omitted multiplication sign in front of a opening bracket have?" So the only way to resolve it absolutely is finding a normative version of that grammar. That's the whole...like 100% core point of this thread. Same as in any language, there can, by definition, never exist any "official" notation of anything. Why? Because, let's say we all agree that 2(9) is the same as 2*(9). But over the course of time, people distinguish between those two, ignoring the "rule". Then the rule itself loses all its meaning...same with grammar/etc. Language - and here ALSO the language of math - is always reliant on the society, the people who use the language. Therefore the OP has rightly shown that the language used in the OP is misleading because it can, in fact, be interpreted both ways. Depending on the "school of thought", if you wanna call it that way, that you are following. In this respect this is a great thread, because it shows the uselessness of official notational rules if the "users" themselves partially ignore them and get so used to a "wrong" notation, that this "wrong" notation in fact becomes "correct". For natural languages that's obviously true. For programming languages it's almost never true. And it would make sense for some mathematical association to define a well defined grammar for mathematical notation. In absence of a normative specification some convention becomes correct one most influential practitioners interpret it the same way.
Well, it depends if we are talking about "programming" languages or about math as a whole. For a programming language you are correct, because this will always give you the exact same result.
But when we think about math as a whole, who "defines" if not the programming language in question has it all wrong?
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On April 08 2011 17:52 MasterOfChaos wrote:
Wikipedia is not normative. And the planetmath link doesn't even touch the subject of omitted multiplication before brackets/variables.
The point of the planetmath link is that it states clearly that there are no rules just convention. The reason we put numbers or whatever in front for parenthese is that it is a shorthand that is convenient since factoring happens a lot in algebra. The multiplication is implied. It depends on the context most of the time in cases like this. There is no actual right or wrong answer here.
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On April 08 2011 17:23 FindMeInKenya wrote:Show nested quote +On April 08 2011 17:11 mcc wrote:On April 08 2011 17:06 FindMeInKenya wrote:
Hierarch trolls pretty hard right now, would anyone topple his domination in trolloing???!!!
Anyhow, unless you never take elementary math, you would know there's only one answer to this question: 288.
I see this not as failure of the writer of the question, but as failure of proper education. Hmm, who is trolling, did you actually read the arguments, seems that you did not. Yes people who have taken elementary math will say it is 288, people who have taken university math and understood what notation is will say that it depends on notation used. Then why do we teach our children the answer is 288? Also, the op did not state any specifics, so we can only read it as is.
Because there is no point in teaching children that it is more complex than it seems. It would be like teaching children relativity from the start instead of starting with Newtonian physics. Yes OP did not state any specifics and that is why both answers can be correct, because we don't know which notation he used. As I wrote 288 is somewhat better answer as it is more mainstream, but the notation that yields 2 is also used quite often and is not just some useless notation created just to prove a point.
Example of useless notation would be : 5 is 2, 77 is 3, + is - .
Notation that yields 2 is standard notation with added rule that implicit multiplication has higher priority than both explicit division and explicit multiplication. That it is just notation is clear from the fact that any expression in standard form can be converted into the "new" one and vice versa.
This shows that new notation is just different graphical representation of the same mathematical relations, but uses different version of order of operations.
Since the OP expression is valid expression in both notations and OP did not specify which notation he used you can only assume/guess which notation he meant.
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After some googling I'm almost convinced that indeed there isn't any "official" mathematical convention like there are for programming languages and engineering standards. Math rules are mostly only "generally" agreed on. But there is no central authority dictating what standards to use.
So I guess that means that "officially", both 2 and 288 are equally wrong, or correct. 48÷2(9+3) is just bad syntax ambiguity.
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Maybe im getting this wrong, but if i get that: 48÷2(9+3)=?
?= 24 12, after all, there is no "*" between the "2" and the "(".
I agree that the most common response would be that it should be a "*", in wich case its 288, but still, if we have a division that is in fact stated by a clear sign, we should have the same for multiplication, right? :D
Just my 2 cents.
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The most boring math problem ever posted on tl.net creates the longest discussion, lots of quarreling about conventions. This is somewhat depressing.
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actually i had it figured out faster than the time it would take me to move the mice over "open new window", so... :D
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On April 08 2011 18:04 jobebob wrote:Show nested quote +On April 08 2011 17:52 MasterOfChaos wrote:
Wikipedia is not normative. And the planetmath link doesn't even touch the subject of omitted multiplication before brackets/variables. The point of the planetmath link is that it states clearly that there are no rules just convention. The reason we put numbers or whatever in front for parenthese is that it is a shorthand that is convenient since factoring happens a lot in algebra. The multiplication is implied. It depends on the context most of the time in cases like this. There is no actual right or wrong answer here.
There is no such thing as "depends on the context" in math.
Convention basically means some set of agreed stardards which are actually rules. All mathematical notations, even +, - etc. are conventions.
Only reason why we use brackets is to avoid "context" and shit, so if there are no brackets then there is nothing we have to talk about. Invisible brackets DO NOT count in math. No context, no shit. It's 288.
Seriously, how fucked up would solving math problems be if everyone could interpret it on his own way.
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«Division and multiplication are equal in priority», read 200 times in the thread, blah blah...
It's not like this you should learn it.
The order between division and multiplications just doesn't matter, and it's quite obvious. For example : 2*2165465498432168749/2... Are you really going to calculate the multiplication first ?
No, and it's the basis of fast mental calculations.
On topic : linear writing is not made for maths anyway.
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I still can not find a support article that show why 288 is more correct than 2 (or the other way around).
It is just "feel right" to do 2(9+3) first for me because the science calculator will do it first, hence, my answer is 2
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On April 08 2011 18:18 Maenander wrote:
The most boring math problem ever posted on tl.net creates the longest discussion, lots of quarreling about conventions. This is somewhat depressing.
People are trying to defend themselves when their egos got hurt when they got it wrong, like the post above yours.
There doesn't have to be a * between the 2 and () its the same concept as 2x.
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Kentor
United States5784 Posts
requoting this. in other words this math problem is retarded and has no real life consequences.
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On April 08 2011 18:23 mr_tolkien wrote:
«Division and multiplication are equal in priority», read 200 times in the thread, blah blah...
It's not like this you should learn it.
The order between division and multiplications just doesn't matter, and it's quite obvious. For example : 2*2165465498432168749/2... Are you really going to calculate the multiplication first ?
No, and it's the basis of fast mental calculations.
You fail. Because in your example 2*2165465498432168749/2 you will get 1 result but if you write it as: 2165465498432168749/2*2 you will get another result which should not be a case with your logic.
Only reason why your first example works is because you can write second part as fraction and then multiplication is with upper part ofc
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On April 08 2011 18:20 bLah. wrote:Show nested quote +On April 08 2011 18:04 jobebob wrote:On April 08 2011 17:52 MasterOfChaos wrote:
Wikipedia is not normative. And the planetmath link doesn't even touch the subject of omitted multiplication before brackets/variables. The point of the planetmath link is that it states clearly that there are no rules just convention. The reason we put numbers or whatever in front for parenthese is that it is a shorthand that is convenient since factoring happens a lot in algebra. The multiplication is implied. It depends on the context most of the time in cases like this. There is no actual right or wrong answer here. There is no such thing as "depends on the context" in math. Convention basically means some set of agreed stardards which are actually rules. All mathematical notations, even +, - etc. are conventions. Only reason why we use brackets is to avoid "context" and shit, so if there are no brackets then there is nothing we have to talk about. Invisible brackets DO NOT count in math. No context, no shit. It's 288. Seriously, how fucked up would solving math problems be if everyone could interpret it on his own way.
Read my earlier post. The point is of course communicating the right equation. But you are wrong, math has some pretty terrible convention. The basic ones are pretty solid of course and should be followed, but for alot of it IS ambigious and DOES depend on context. Writing down an arithmatic operation is not math. The reason most people find this confusing is that the 2(9+3) should never come up anyways. Pulling number out of the parenthese is convention for when you are doing algebra and factoring. when you have 9x+3y then it makes sense to write it as 3(3x+y).
Notation is important but people need to realize they are just instructions to represent ideas or operations.
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On April 08 2011 18:25 pedduck wrote:
I still can not find a support article that show why 288 is more correct than 2 (or the other way around).
It is just "feel right" to do 2(9+3) first for me because the science calculator will do it first, hence, my answer is 2
see thats your problem, stop doing everything by a calculator and learn order of operations. The calculator can't get it right if you input it wrong you know?
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On April 08 2011 18:25 pedduck wrote:
I still can not find a support article that show why 288 is more correct than 2 (or the other way around).
It is just "feel right" to do 2(9+3) first for me because the science calculator will do it first, hence, my answer is 2
it seriously doesn't matter what you "feel right" if you don't know anything about math.
and I doubt that any decent calculator that uses standard notation will calculate it that way.
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On April 08 2011 18:27 Kentor wrote:requoting this. in other words this math problem is retarded and has no real life consequences.
requoting this because it says in it:
An example is the convention known as
the Rules for the Order of Operations, introduced into the school curriculum in
the fith or sixth grade:1
(1) Evaluate all expressions with exponents.
(2) Multiply and divide in order from left to right.
(3) Add and subtract in order from left to right.
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On April 08 2011 18:28 bLah. wrote:Show nested quote +On April 08 2011 18:23 mr_tolkien wrote:
«Division and multiplication are equal in priority», read 200 times in the thread, blah blah...
It's not like this you should learn it.
The order between division and multiplications just doesn't matter, and it's quite obvious. For example : 2*2165465498432168749/2... Are you really going to calculate the multiplication first ?
No, and it's the basis of fast mental calculations. You fail. Because in your example 2*2165465498432168749/2 you will get 1 result but if you write it as: 2165465498432168749/2*2 you will get another result which should not be a case with your logic. Only reason why your first example works is because you can write second part as fraction and then multiplication is with upper part ofc
I don't know what to say. 2*2165465498432168749/2 = 2165465498432168749/2*2 = 2/2*2165465498432168749. That's the point of my message, which was on how you have to see the "order" of calculations, especially between divisions and multiplications.
You do multiplcation/divisions at the same time because it doesn't matter.
There is a REASON behind this order. You do them before additions and substractions because it would cause some randomness the other way around.
So please refrain from starting posts with «You fail» on TL as from now.
As for 1/2x, everybody reads it as 1/(2x) because of the fact that 2 is seen as a mere factor of x, it's not shocking or anything. Stop mindfucking yourselves please.
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On April 08 2011 18:20 bLah. wrote:Show nested quote +On April 08 2011 18:04 jobebob wrote:On April 08 2011 17:52 MasterOfChaos wrote:
Wikipedia is not normative. And the planetmath link doesn't even touch the subject of omitted multiplication before brackets/variables. The point of the planetmath link is that it states clearly that there are no rules just convention. The reason we put numbers or whatever in front for parenthese is that it is a shorthand that is convenient since factoring happens a lot in algebra. The multiplication is implied. It depends on the context most of the time in cases like this. There is no actual right or wrong answer here. There is no such thing as "depends on the context" in math. Convention basically means some set of agreed stardards which are actually rules. All mathematical notations, even +, - etc. are conventions. Only reason why we use brackets is to avoid "context" and shit, so if there are no brackets then there is nothing we have to talk about. Invisible brackets DO NOT count in math. No context, no shit. It's 288. Seriously, how fucked up would solving math problems be if everyone could interpret it on his own way.
Point is there actually are two slightly differing conventions in use and they agree on all well written expressions, but on the OP expression they differ and give each of the answers presented. That is why such expressions are avoided like fire in serious math texts. That said one is standard that gives 288, second one is slight variation that is actually used a lot at least in my uni probably to save some parenthesis and make expressions slightly more aesthetic.
There are actually even more differing conventions, but OP expression does not satisfy any of them so we can ignore them. And the notation used is mostly inferred from the context of the work (distinctive look of the convention, theme of the work, preference of the author) or sometimes explicitly stated.
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The important thing to take away from this thread is not what the correct order of operations is, but that you should NEVER write an expression like that.
48(9+3)/2
On April 08 2011 09:34 mahnini wrote:
if the equation was 4 + 5 * 3 no one would answer 27
27 would be the expected answer in Smalltalk.
On April 08 2011 11:31 space_yes wrote:
Yes we do interpret 1/xy as (1/x)*y
The only reason to write y/x as 1/xy is if you're trolling, don't do it in a paper you want published.
On April 08 2011 11:52 Zeke50100 wrote:
An ambiguous question would be "What is f(x)".
However, the OP's question is still not ambiguous, because 2(9+3) is not a single term >.>
Is the function 2(x) defined anywhere?
If it were, wouldn't the function evaluation take precedent over * / ?
On April 08 2011 15:57 chonkyfire wrote:
Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.
16/{2*[8-3(2)]+1}
16/{2*[2]+1}
16/5
3.2
P.S. how do people get the "÷"? I have to use cut/paste.
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EPT
