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On April 08 2011 09:01 Zeke50100 wrote:Show nested quote +On April 08 2011 08:54 munchmunch wrote:On April 08 2011 08:44 Zeke50100 wrote:On April 08 2011 08:40 munchmunch wrote:On April 08 2011 08:18 MandoRelease wrote:On April 08 2011 08:04 munchmunch wrote:On April 08 2011 08:02 Zeke50100 wrote:On April 08 2011 08:01 munchmunch wrote:
[
Not due to laziness at all, actually. Granted, it would be incorrect to omit the parentheses in many contexts, but in any context where it can be expected to be unambiguous to the reader, it would be recommended to any mathematical writer to drop the parentheses for aesthetic reasons.
Being accustomed to the omission of parentheses doesn't make it right  No, but aesthetics can be a good reason. Not in anything that does not involves advanced mathematics. I certainly agree that you sometime need to lower your accuracy when you write advanced mathematical paper in order to make it understandable. It is not the case for basic math like trigonometry and basically anything put on a non mathematical forum. For these, it's only lazyness because adding parentheses here and there would not make it any less clear, so aesthetics is not always a good reason. Ok, I guess I should write a longer post on my thoughts on this subject. Recall that the original subject was about whether something like cos 2x is an incorrect statement for cos(2x). There is no doubt that it is helpful for beginning students to put the brackets in. And every student should understand that there is an unambiguous idea, essentially "perform the multiplication 2 * x and then evaluate the function cos at 2*x", which can be communicated unambiguously by adding the brackets. It would also be nice if people knew that this statement can be made so clear that a computer can understand it, although a computer might require something like "cos(2*x)" or "(cos (* 2 x))". However, none of that means that cos 2x is wrong! My emotion towards people who perpetuate this sentiment is similar to that contained in Stephen Fry's language rant. As long as the notation is understood, it is never wrong to write cos 2x. And it can sometimes be better to write cos 2x. In differential geometry, for example, if you add parentheses everywhere they might be required, the large amount of parentheses can impede readability. This is not to contradict you; no doubt cos(2x) is a better choice for a homework thread on TL, for example. But that just means that other considerations are preeminent in that situation. The problem is that cos2x is NOT equal to cos(2x). It IS wrong. It's not comparable to Fry's language rant at all, because there is a right and a wrong when it comes to math and mathematical notation. This is exactly the sentiment that I find disgusting. I mean, I agree with you to a point. But the idea that cos 2x is not equal to cos(2*x), when many people use cos 2x without the slightest ambiguity, is perverse to me. But let's agree to disagree. If we keep arguing, it can only go two ways: into ad hominem, or into a dick showing contest, neither of which is agreeable to me. And I hope you saw my apology for starting on the ad hominem's earlier. They use cos2x without ambiguity because people understand what is right. I would be fine with that if EVERYBODY understood what is right, but obviously not. People who pass on the incorrect notations may not have bad intentions (I omit parentheses myself sometimes when communicating with somebody who knows what I mean), but people who don't know better pick up on it and think it's right. They try putting it into a calculator, and guess what happens?
Almost time for me to quit the thread. Will do a few more rounds.
As a philosophical exercise, let's assume that you have no opinion about whether cos 2x is equivalent to cos(2x). What procedure would you propose to check whether or not the two are equivalent?
Here's mine in spoilers:
+ Show Spoiler +
1. Understand that the question must be phrased in terms of some community, say mathematicians, elementary school teachers, computer programmers, etc.
2. Check whether or not the custom is consistent with other customs of the community.
3. Check whether or not there is positive evidence that the community engages in such a custom.
A positive answer for 2 and 3 indicates correct usage.
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On April 08 2011 09:05 mahnini wrote:
this is like asking what word represents "you are", you're or your?
given the correct context "your" can easily be interpreted as "you're" but that doesn't mean "your" is correct.
example: your wrong.
Not really the same. The question is complicated by there being ambiguities caused to anyone who has studied math by the question's leaving out brackets. Because a maths question will never be written like this beyond a certain level it is designed to trick people, and really comes down to where the person attempting it decides to insert the brackets. The question is almost meaningless in this notation.
You're and your are completely different words with different definitions. No ambiguities are caused by using your unless it is different in America to the UK.
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No one would interpret 48 / 2 * (9+3) as anything but 24 * 12 = 288, or 1 / 2 * x as anything but x/2. However, when you use juxtaposition to sub for multiplication, it is frequently understood that you are collecting 2(9+3) or 2x into one unit.
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On April 08 2011 09:03 garbanzo wrote:Show nested quote +On April 08 2011 08:59 Zeke50100 wrote:On April 08 2011 08:52 garbanzo wrote:On April 08 2011 08:50 Mailing wrote:On April 08 2011 08:49 Zeke50100 wrote:On April 08 2011 08:47 garbanzo wrote:On April 08 2011 08:39 Zeke50100 wrote:On April 08 2011 08:38 Entropic wrote:
lol what a shittily written and ambiguous expression (as many have noted already) It's 0% ambiguous, but 100% a test of your understanding of math. You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)? How about 1/2(a+b) versus 1/2*(a+b)? There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity. If you can find some evidence of this.. Yes, I would like some source that it can definitively only be read one way. And you didn't really answer my question. If you were to ask someone a question, and you wanted absolutely no confusion, then would you consider choosing one notation over the other? I think you're lying to yourself if you say otherwise. I don't get how "these two things are exactly the same" do not equate to "these two things are interchangeable, and therefore one is no more ambiguous than the other" in your mind. Okay, I concede. Next time a peer reviewer in a journal or professor tells me to rewrite an equation because it's ambiguous, I'll just tell them to learn their order of operations. Edit: My comment isn't meant to be sardonic. I'm just trying to point out that just because there is a grand rule that you can always refer to, e.g. order of operations, doesn't mean that certain ways of writing an equation are superior because they remove ambiguity.
Both forms are equally simplified, and both mean exactly the same thing. Just because you prefer one way doesn't mean one is more ambiguous. There is no ambiguity >.>
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On April 08 2011 09:12 mahnini wrote:Show nested quote +On April 08 2011 09:06 Mailing wrote:On April 08 2011 09:04 buhhy wrote:
This thread makes me both super rage and facepalm. Pretty sure most university math kids will see 1/2x as 1/(2x). Either way, I always err on the side of more brackets to be clear.
Also someone post the link to the bodybuilding thread? I don't see it anywhere? This thread makes it pretty clear that different countries teach different math... which is fucking weird. In the US, 1/2x = 1/(2x)... in some it = .5x that's wrong. generally books will write it as ½x and use / to only mean simple division but just because you are used to a certain method of interpreting the symbol doesn't mean it is empirically correct. when you read single line equations the standard interpretation follows the order of operations.
Actually, he is right. Different typesetting conventions are more or less common around the world. In France, for example, it is common to apply functions on the right side of an argument, eg. x T rather than Tx.
Also, the notion of an inline fraction is pretty well accepted. They are used when you don't want to interrupt the flow of a large block of text just to write a single fraction.
EDIT: changed "inline expression" to "inline fraction"
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On April 08 2011 09:18 Severedevil wrote:
No one would interpret 48 / 2 * (9+3) as anything but 24 * 12 = 288, or 1 / 2 * x as anything but x/2. However, when you use juxtaposition to sub for multiplication, it is frequently understood that you are collecting 2(9+3) or 2x into one unit.
This.
Now, can someone post the bodybuilding link? Why did it get removed?
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On April 08 2011 09:15 Piy wrote:Show nested quote +On April 08 2011 09:05 mahnini wrote:
this is like asking what word represents "you are", you're or your?
given the correct context "your" can easily be interpreted as "you're" but that doesn't mean "your" is correct.
example: your wrong. Not really the same. The question is complicated by there being ambiguities caused to anyone who has studied math by the question's leaving out brackets. Because a maths question will never be written like this beyond a certain level it is designed to trick people, and really comes down to where the person attempting it decides to insert the brackets. The question is almost meaningless in this notation. You're and your are completely different words with different definitions. No ambiguities are caused by using your unless it is different in America to the UK.
it's perfectly readable except people some people are used to reading it within a different context.
2 / 3(4) is more clearly (2 / 3) * 4, but people are using 2 / 3 (4) to represent 2 / [3(4)]
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This is a pretty effective linguistics teaser. The equation is just the form in which it is been delivered. Bravo!
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On April 08 2011 09:07 jalstar wrote:48/2(9+3) If 2(9+3) is computed first it has to satisfy the laws of the natural numbers. So 48/18 + 6 should equal 48/24 by the distributive property. But 9.6666667 != 2. So by the natural number system properties, 48/2 must be computed before 2(9+3), giving you 288. All of those who answered "because that's the way it is!" without any sort of proof attempt make me 
Is that some attempt at a joke, just a troll, or what?
Your reasoning isn't logical. If you had to compute 2(9+3) first, even then it would result in (18 + 6) not 18 + 6.
Secondly, where did the 2 come from with regards to "!= 2"? Just because it's an option in the poll doesn't mean it is necessarily the only other possible answer.
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On April 08 2011 09:03 munchmunch wrote:Show nested quote +On April 08 2011 08:59 Zeke50100 wrote:On April 08 2011 08:52 garbanzo wrote:On April 08 2011 08:50 Mailing wrote:On April 08 2011 08:49 Zeke50100 wrote:On April 08 2011 08:47 garbanzo wrote:On April 08 2011 08:39 Zeke50100 wrote:On April 08 2011 08:38 Entropic wrote:
lol what a shittily written and ambiguous expression (as many have noted already) It's 0% ambiguous, but 100% a test of your understanding of math. You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)? How about 1/2(a+b) versus 1/2*(a+b)? There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity. If you can find some evidence of this.. Yes, I would like some source that it can definitively only be read one way. And you didn't really answer my question. If you were to ask someone a question, and you wanted absolutely no confusion, then would you consider choosing one notation over the other? I think you're lying to yourself if you say otherwise. I don't get how "these two things are exactly the same" do not equate to "these two things are interchangeable, and therefore one is no more ambiguous than the other" in your mind. LOL, I read that and thought "What a good post, well said!" Then I reread it and realized you were saying the exact opposite of what I thought. I guess a Zeke50100 is an anti-munchmunch. And to jump into that conversation, "the same" on a semantic level is not the same as being "the same" on a syntactic level.
Syntax doesn't mean a thing when it comes to ambiguity because it should be understood that both are simplified to the same level. You're suggesting that "2+1-1" would be more correct than "2-1+1" because it's syntactically more "natural" to somebody's own perception, which is what garbanzo is trying to say.
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I voted for 2, then realized what its supposed to be.... -_- Thanks high school
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On April 08 2011 09:13 dmillz wrote:
Why are people so surprised by how many people got this wrong? From my experience the vast majority of people are horrible at math, no matter how simple it may seem to those who understand it. All you need to know to solve those equations is BEDMAS which is an elementary school concept.
But it has nothing to do with math skills. It is like saying that if you do not know chess notation you cannot be good at chess.
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Mathematical/linguistic rules are not a good way to justify correctness. (meaning pedmas or w/e is not an acceptable defense)
Notation is subjective, there is no such thing as correct or incorrect notation. You can redefine any convention, notation, language, etc in any way you want because they are all arbitrary constructs to begin with
If you're personally solving the problem, you can use 48&2@9#3 or w\jx(ptE) or even weiogheroighjtoh940tiuojeithdiohj5hj if you like
If you do not know your target audience, using massive amounts of parenthesis ((48)/(2))*(9+3) is more likely to result in your idea being communicated successfully, but that doesn't make it more correct
Either answer can be correct depending on how individuals interpret the expression, because under different conventions, the expression means different things
Edit: Maybe it's just a regional thing, but is maths actually acceptable to say anywhere? it makes me cringe xP lol
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The problem is that wolfram is an interpreter, and not math itself, which is why it's not the best source for evidence XD
Although I have to say it is interesting to see people who voted in a contradictory manner. I'm proud to say I didn't accidentally click the wrong one because the answers are listed in a different order than the poll results show :D
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I had a math teacher for high school who sometimes wrote cos x^2 without brackets, and I just couldn't tell what he meant: (cos x)^2 or cos(x^2).
I think a problem is that you want your equations to be presentable and the order of operations is just a trick we use to prevent cluttering them with brackets. Another way to make clear what happens is to use special symbols to let the reader get a good impression which 'components' are interacting with eachother, or what abstract concept is expressed by this equation.
If you want to have x/2, generally you'll use a special 1/2 symbol just to make this clear, then. And 1 / (2x) will have the horizontal line dividing it, making it even more unambiguous.
I have honestly never seen a slash used beyond very simple equations in any textbook, as far as math goes it's just used more for like informal writings since it's the ascii representation for the horizontal line. I know it has a different meaning for a calculator, since there it does mean x/2, but if you read 1/2x as an informal representation it's easy to imagine it does mean 1/(2x). Even if technically it's wrong. The way the question is phrased however, leads you to believe it's more informal.
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Jesus fuck, it doesn't matter what the god damn answer is.
If you can figure out what 48/( 2*(9+3) ) or what (48/2)*(9+3) then you can do the problem no matter what god damn way they meant it.
Stop wasting bytes on this lovely websites server with your stupid fucking dipshit arguments.
IT
DOESNT
FUCKING
MATTER.
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So is this like 'pemdas taught people' being incorrectly taught that multiplication comes before division.
I feel part of this debate is bedmas vs pemdas.
:S
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I learned PEMDAS
Please Excuse My Dear Aunt Sally
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
I was taught that M and D are interchangeable
and A and D are interchangeable
You do whatever is on the left first
So:
48÷2(9+3)=48/2*12
48/2*12= 24*12
24*12= 288
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multiplication and division have the same jerarquy and are read from left to right so should it be:
48/2(9+3)
24 x 12
188
Dont confuse that X with vectorial multiplication i meant just multiplication
and in the second case they dont tell you if 2 or x are in parenthesis or something like that so following the same rule from left to right the answer is
1/2x
(1/2). x
x/2
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EPT
. If you put in "1/2 x":![[image loading]](http://i52.tinypic.com/214a03o.png)
![[image loading]](http://i51.tinypic.com/uc8pi.png)
![[image loading]](http://i52.tinypic.com/mr3cr4.png)
