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On April 08 2011 18:03 sleepingdog wrote:Show nested quote +On April 08 2011 17:59 MasterOfChaos wrote: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?
Yeah. Programming languages obviously make rules of their own so to speak to make sure any expression is unambiguous. But math is actually like a natural language that has evolved as a natural language over the course of history.
There's plenty of competing notations available for more complex expressions than those only involving +-*/ . Also, math people are lazy so they often dedicate some space to explain the specific notation they will use in a paper to make sure the reader will understand. Say one paper using a new type of notation gets vastly influential; obviously the notation used in it will gain influence.
It's quite a mess actually.
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why would people think 1/2x = (1/2)x? if you wanted to write that why wouldn't you put x/2 ???
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On April 08 2011 15:57 chonkyfire wrote:
Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.
When using the normal precedence rules, you get 17. When using the sloppy notation you get 5, but note that there's additional spacing around the middle term to indicate a stronger binding (this, together with larger slashes, are almost always used as visual clues in that sloppy notation; at least as far as I have experienced and used). But the question in the OP has neither, which resolves the ambiguity.
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+ Show Spoiler +On April 08 2011 19:06 dthree wrote:
why would people think 1/2x = (1/2)x? if you wanted to write that why wouldn't you put x/2 ??? because it's not the question how you could write it differently. With the same argument you could say why would people think 1/2x = 1/(2x) when they could just write it like that 1/(2x). In fact, 1/2x = (1/2)x is correct. Tho I would usually still interpret it as 1/(2x). I don't know why. :/
edit: nvm. seems like both are correct. I should read the whole thread next time.
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On April 08 2011 19:16 Keniji wrote:Show nested quote +On April 08 2011 19:06 dthree wrote:
why would people think 1/2x = (1/2)x? if you wanted to write that why wouldn't you put x/2 ??? because it's not the question how you could write it differently. With the same argument you could say why would people think 1/2x = 1/(2x) when they could just write it like that 1/(2x). In fact, 1/2x = (1/2)x is correct. Tho I would usually still interpret it as 1/(2x). I don't know why. :/
Aren't you supposed to write everything in its most simplified form? x/2 would be most simplified but 1/(2x) is not... right?
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On April 08 2011 19:16 Keniji wrote:Show nested quote +On April 08 2011 19:06 dthree wrote:
why would people think 1/2x = (1/2)x? if you wanted to write that why wouldn't you put x/2 ??? because it's not the question how you could write it differently. With the same argument you could say why would people think 1/2x = 1/(2x) when they could just write it like that 1/(2x). In fact, 1/2x = (1/2)x is correct. Tho I would usually still interpret it as 1/(2x). I don't know why. :/ If you missed the thread, both are correct. There's no official convention. What you should really do, is put the parenthesis where you should to make it clear what you mean.
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Ok, here's my take on this.
Google, Wolfram, C#, Casio fx-991ES, Android Calculator says 288.
My brain is screaming 2.
Here's a way how I got to 2: ![[image loading]](http://i.imgur.com/SZrfJ.gif) .
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On April 08 2011 18:37 mr_tolkien wrote:Show nested quote +On April 08 2011 18:28 bLah. wrote: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.
But if division and multiplication are equal in priority and if the order doesn't matter you can read 2165465498432168749/2*2 like 2165465498432168749/4. The order does matter, you have to do the division first. I think that's what he wanted to say.
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There's actually 2 different definitions of divison, with two different fields (http://en.wikipedia.org/wiki/Field_(mathematics)). The first is the arithmetic definition where everything is strictly left to right, unless there's an explicit parenthesis. The second is the algebraic definition where you'd implicitly assume a parenthesis, and 1/abc = 1/(abc). If you were doing geometry then division isn't even defined, and the equation is meaningless. And if you want you can make up whatever crazy definition you want, for division.
If you insist on picking a single correct answer, I'd argue that the arithmetic definition (which gives 288) is more correct here, since nobody uses the ÷ sign for doing algebra. Apparently it's called an "obelus" lol. The fraction bar is called a "vinculum". How do you even type ÷, anyway? Is everyone just copy pasting it like I did?
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On April 08 2011 19:06 dthree wrote:
why would people think 1/2x = (1/2)x? if you wanted to write that why wouldn't you put x/2 ???
Exactly, unless you're trying to trick someone there is no reason to write x/2 as 1/2x, and so any occurrence of 1/2x can be pretty safely assumed to be shorthand for 1/(2x).
In physics texts, when the units of permittivity are given as "C^2 / N m^2", they mean "C^2 N^-1 m^-2", if they meant "C^2 m^2 / N" they would have written that.
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I have no idea if im right or wrong on this one Im super terrible at math and have little education in it but when i did this problem i knew how to do it (i think). i answered the 288 one with "And I'm not studying" but i continued to read the thread to figure it out but everyone seems to be unsure/arguing about it? So i googled the problem and it said 288, so i guess thats right?
The bottom one with the 1/2x any time i see a number next to a letter i always feel like i was taught that always implies multiplication. so 1/(2*x) would seem to be the only viable way to look at it? i don't understand the "/" from memory i would say iv never seen that in a problem in a book i had but who knows that was YEARS ago D:
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my calculator says the answer is 2. i typed it in exactly as the thread has it, and did it twice.
if i type it into my calculator as 48/2(9+3) the answer is 288. however that's not what the question asked as there is clearly a divide by symbol
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In Microsoft Windows, the obelus is produced with Alt+0247
÷
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here's how I would do it, as someone who has never been to college and took the easiest/fewest math courses possible in high school.
48/2(9+3)
48/2*12
24*12
288
is this right
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On April 08 2011 05:59 n00b3rt wrote:
I'm seriously losing faith in humanity here
lol what's up with people insulting others for thinking it's 2? don't act like all 4th graders would have gotten this right because the equation is written in a way to deceive you.
pathetic. keep stroking your egos and thinking you're better than someone who gets this wrong. tbh i probably would've gotten this wrong if it wasn't in this context. if this wasn't asked like it was a trick question i wouldn't have stopped to re-evalute.
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Other than elementary school teachers, no actual science is ever done with mathematics read left to right. The obelus is not used after about second grade arithmetic (exactly because it is ill defined!) and algebraic division always implies the start of the denominator (as a shorthand in typed text for the vinculum which acts **as though the entire denominator is in brackets**).
Nobody in their right mind would ever write : 48÷2(9+3)
If you wanted to express "288" you would write (48/2)(9+3)
If you wanted to express "2" you would write 48/(2(9+3))
I would guess that the reason many perfectly mathematically literate scientists and engineers would guess the "wrong" answer is that the question is digging up archaic forms of arithmetic which are simply not used in the real world. Mathematics has evolved into a much more precise form than is taught to elementary school children and for good reason. The results of this poll should be evidence not that educated people don't know what they are doing, but that the question is formulated in a poor and antiquated manner.
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On April 08 2011 19:54 radialis wrote:Show nested quote +On April 08 2011 05:59 n00b3rt wrote:
I'm seriously losing faith in humanity here lol what's up with people insulting others for thinking it's 2?
Probably because not only do they fail to realize the debth of the problem, but also they are incapable of reading this thread. They should at least guess that there's more to it if the thread already has accumulated such a high page-count...
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without the * its 2 if you add a * its 288. All people who got 288 are dumb. Just try with your calculator if you dont believe me. 48/2(9+3) is actually like someone already said.
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I fail to se how this is remotely interesting...
What I though of after reading the question :
http://xkcd.com/169/
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On April 08 2011 19:56 jgad wrote:
Other than elementary school teachers, no actual science is ever done with mathematics read left to right. The obelus is not used after about second grade arithmetic (exactly because it is ill defined!) and algebraic division always implies the start of the denominator (as a shorthand in typed text for the vinculum which acts **as though the entire denominator is in brackets**).
Nobody in their right mind would ever write : 48÷2(9+3)
If you wanted to express "288" you would write (48/2)(9+3)
If you wanted to express "2" you would write 48/(2(9+3))
I would guess that the reason many perfectly mathematically literate scientists and engineers would guess the "wrong" answer is that the question is digging up archaic forms of arithmetic which are simply not used in the real world. Mathematics has evolved into a much more precise form than is taught to elementary school children and for good reason. The results of this poll should be evidence not that educated people don't know what they are doing, but that the question is formulated in a poor and antiquated manner.
and
On April 08 2011 19:06 dthree wrote:
why would people think 1/2x = (1/2)x? if you wanted to write that why wouldn't you put x/2 ???
It's a troll question. Would you really start a TL thread and ask:
x/2 = ?
a) 1/2x
b) 1/(2x)
Alternatively would you start a TL thread and ask:
(48/2)(9+3) = ?
a) 2
b) 288
No you would get warned and possibly banned. I understand people are confused but the most frustrating aspect of this thread is the ridiculous number of people complaining the notation is ambiguous or poorly written.
What the fuck seriously. The whole point of the question(s) is for you to resolve the ambiguity (using order of operations). It's written in a purposefully confusing way.
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EPT
