9/3(4-1) another one of those stupid maths thing Watch

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JoMo1
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#21
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#21
(Original post by eliotball)
No, you are wrong, it is not ambiguous, multiplication and division happen left to right. This is a standard rule and is also how computers operate.
No. It. Doesn't. All mathematical operators of the same type happen simultaneously, division is the same type of operator as multiplication as, for example, 3/4 is shorthand for 3\times\frac{1}{4} which in turn is shorthand for 3\times4^{-1} otherwise known as the multiplicative inverse of 4. They multiplication and division are the same thing written 2 different ways.

As is the answer to all of these types of thread:

9/3(4-1) = 7*7+ = absolutely nothing, it's a completely meaningless statement. Maths is just like language, you can't just stick 2 words together and make something that makes sense, even if it sounds/looks a bit like it should, just like \frac{1}{0} or "To chip hand too and for to to to eleven fourteen but and canteen"
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SmileyGurl13
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#22
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#22
(Original post by Deema)
The answer is 9.

Always remember BIDMAS/BODMAS!!!!
Brackets
Indices / Other
Division
Multiplication
Addition
Subtraction

Come on OP, this is SATs maths
Seriously... lol you're going to get negged :P
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munn
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#23
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This is actually Euclid's proof for 9=1.
It's in book 4 of Elements for anyone who cares to look
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nuodai
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Ah yes, Planet Math, the decider of notational standards. How could I be so stupid.
Mechie
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(Original post by nuodai)
TSR needs to install something to detect threads with anything of the form a/b(c+d) in the title, stamp the words [COLOR="Red"]AMBIGUOUS NOTATION[/COLOR] over any other mention it and then print out a massive hand to slap the OP with.

This thread will soon be locked and deleted, making my post redundant, so I won't put any effort into justifying my claim that the notation is ambiguous, but it is. You're wrong if you claim that it's definitely and unquestionably one answer or the other. There are implicit brackets, meaning that either a/b(c+d) = (a/b)(c+d), or that a/b(c+d) = a/(b(c+d)). That is, \frac{a}{b}(c+d) or \frac{a}{b(c+d)}. It's not made clear from the notation which it is, and you can't decide conclusively without making up a non-standard rule (e.g. 'work from left to right'). This is why people who don't know any better go with their first instinct and the battle commences.

The real question is this. Why won't it stop?!

(Original post by nuodai)
No, that isn't a standard rule, it's a method used to make Year 8 pupils ask less questions when presented with something like 2×3×6×12 to evaluate, and the rule doesn't exist outside of the world of KS3 maths.

Notation serves to make our lives easier, and any rules which refer only to notation (e.g. 'work left to right') are not mathematical rules, they're guidelines for notation and are open to interpretation depending on what notation you use. In fact, if I wrote 1+x/3+x I'd expect it to be interpreted as \frac{1+x}{3+x} instead of 1 + \frac{x}{3} +x.

"9/3(4-1)" is written ambiguously; it can have no evaluation until it is clarified.

And for what it's worth, computers don't uniformly operate like that. There are differences even between different programming languages, where some work from right to left, for example. And computers operate in the way they were programmed -- computers can't deal with ambiguity and so the options are either to present "ERROR" or to interpret it in one way or the other. If a computer interprets an ambiguous statement in one particular way, it doesn't mean that way is right, it just means that it defaults to a particular interpretation of the statement.
I love these answers. Thank you.
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JoMo1
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#26
(Original post by nuodai)
Ah yes, Planet Math, the decider of notational standards. How could I be so stupid.
I don't think I've seen a maths website be so spectacularly wrong before...
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mc_watson87
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#27
(Original post by nuodai)
. In fact, if I wrote 1+x/3+x I'd expect it to be interpreted as \frac{1+x}{3+x} instead of 1 + \frac{x}{3} +x.
If i wrote: 1+x/3+x I'd hope it would be interpreted as I wrote it, not in some similar but completely wrong manner. Lets hope you never write exam papers then...
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JoMo1
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(Original post by mc_watson87)
If i wrote: 1+x/3+x I'd hope it would be interpreted as I wrote it, not in some similar but completely wrong manner. Lets hope you never write exam papers then...
What makes it completely wrong? Indeed, I'd assume 1+x/3+x would be interpreted differently from what Nuodai states, but his isn't wrong. BIDMAS/BODMAS is the only point of reference for these problems and they are absolutely meaningless in actual mathematics, more a guideline for how it should be written pre-university.

In actual fact, I have written quotients exactly like that and then gone and clarified with brackets later on, but it has to be understood that notation is there to convey a theoretical idea to another person, not to define your idea. Using bad notation isn't wrong, it's bad communication as notation is a completely arbitrary thing. I can rename the natural numbers less than 10 to start at 7, finish at 4 and have "cat" in the middle. Doesn't make me wrong, it's just a bit pointless.
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StephenNeill
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#29
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Weirdly, today's Spiked Math comic ( http://spikedmath.com/415.html ) was:


Personally I agree that the above is too ambiguous to be allowed, and we should just leave it there.
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nuodai
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(Original post by mc_watson87)
If i wrote: 1+x/3+x I'd hope it would be interpreted as I wrote it, not in some similar but completely wrong manner. Lets hope you never write exam papers then...
Or rather, let's hope exam papers are never written in plain text (ambiguities of this nature are cleared up by LaTeX and similar text formatting software).

But regarding your first point, I think you're misunderstanding the whole point of notation -- to make it clear what you mean. Introducing arbitrary rules which are applied mechanically to every expression you see completely voids this point, hence my 1+x/3+x example. "Wrong" is when it's not clear, "right" is when it is. If someone wrote a question here asking how to split x/(3+x)(1+x) into partial fractions it would be clear that they meant \frac{x}{(3+x)(1+x)} instead of \frac{x}{3+x}(1+x)}, for example. If it's clear what you mean from the context then there is no problem in writing it. And there's no avoiding context in maths; if you study maths to a higher level than, say, GCSE, you'll come across things like functions, where people may write f^2(x) to mean f(x) \times f(x) or f(f(x)) or \frac{d^2f}{dx^2}, but it's almost always clear from the context (and when it's not clear, you say what you mean).

Here we have no context. No context, no meaning.
mc_watson87
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(Original post by JoMo1)
What makes it completely wrong? Indeed, I'd assume 1+x/3+x would be interpreted differently from what Nuodai states, but his isn't wrong. BIDMAS/BODMAS is the only point of reference for these problems and they are absolutely meaningless in actual mathematics, more a guideline for how it should be written pre-university.

In actual fact, I have written quotients exactly like that and then gone and clarified with brackets later on, but it has to be understood that notation is there to convey a theoretical idea to another person, not to define your idea. Using bad notation isn't wrong, it's bad communication as notation is a completely arbitrary thing. I can rename the natural numbers less than 10 to start at 7, finish at 4 and have "cat" in the middle. Doesn't make me wrong, it's just a bit pointless.
It's wrong bro 1 + x/3 + x is exactly what is stated on the tin. Notation is not completly arbitary... are you from another planet? Notation is defined.

For example if 1 + x/3 + x === 5, x === 3

It's simple maths, x does not equal -14/4, as Nudo might hope.
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JoMo1
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#32
(Original post by mc_watson87)
It's wrong bro 1 + x/3 + x is exactly what is stated on the tin. Notation is not completly arbitary... are you from another planet? Notation is defined.

For example if 1 + x/3 + x === 5, x === 3

It's simple maths, x does not equal -14/4, as Nudo might hope.
Notation is locally defined. What if you're going to be saying something ambiguous, you define it for the particular piece you are writing. If I'm doing a problem sheet for an Oxford tutor I can write S in the context of Markov Chains and they'll know I mean the state space, because that's how we notate it in that particular course. If I go over to cambridge, I'd have to define it, as they might use S to mean the chain itself, or use I to denote the state space. Notation generally makes sense and then we stick with it in the assumption that people are going to follow us, but it is not set in stone, and never will be because to do so would be incredibly pointless.

Also, Nuodai actually wrote 1+x/3+x, you have written the same with spaces to emphasise the differences. Internet wise, that's a vaguely adopted notation as it copies the way of spoken maths of grouping the terms together that you wish to be processed first. This does not make yours any difference, you're just removing some of the ambiguity so almost everyone will know what you mean. However, the 1+x/3+x can be parsed to an equally valid expression 1+x / 3+x.

From your: "It's what it says on the tin" argument I'm going to assume you're not doing a maths degree. I have almost 2 years training in formal mathematics; Nudoai, I believe, has more. We're telling you that it's a matter of localised definition, not universally defined notation and have given plenty of examples and reasonings for why this is the case. You're argument seems to consist of: Well this is the way I do it.
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Blazara
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#33
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#33
(Original post by eliotball)
No, you are wrong, it is not ambiguous, multiplication and division happen left to right. This is a standard rule and is also how computers operate.
What about arabic computers?
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Aaargh
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#34
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It's both and it's neither. It's the mathematical equivalent of drawing a circle on a piece of paper and asking someone if it's an 'Oh' or a zero; which one was it meant to be? If you meant it to be (9/3)(4-1) then it's 9, if you meant it to be 9/(3(4-1)) then it's 1. You can't change the result of a sum by writing it badly...
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Jimbo1234
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(Original post by SmileyGurl13)
People keep saying it's 1 cos 4-1 = 3 and 3 * 3 = 9 and 9/9 = 1, which is all true but if that were the correct method wouldn't it need to be 9/(3(4-1)).

OKAY i'm sorry I just wanted to make sure I wasn't missing something cos everyone was saying 1.
It is too ambiguous.

Is it 9 / (3(4-1))

OR

(9/3) * (4-1) ???
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Xx.MissEG.xX
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(Original post by Bobifier)
Contrary to popular belief, it does not make you cleverer than someone to ask them to solve an ambiguous statement and for them to get a different answer to you.
I am really curious, what is your sig meant to mean?
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Arianto
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#37
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42.
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Bobifier
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(Original post by Xx.MissEG.xX)
I am really curious, what is your sig meant to mean?
This link should explain everything.
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Dragon
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#39
(Original post by nuodai)
The real question is this. Why won't it stop?!
Because it's a meme/it sparks arguments/it's a good way to troll. This is the third TSR thread I've seen like this (there may have been more) and the arguments are still going strong.
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Rascacielos
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#40
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I'd go for 1.

Edit: What on earth, it's an ambiguous question, it could be either 1 or 9, but the way I see it, it's 1. Neg reps not appreciated here.
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