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Would you try actually contributing to the discussion for once instead of trying to insult people?
you are thinking of / as the bar accomplishing the following :
however, "/" does not accomplish that here
I agree--I've already said I think that as written, the expressions we're talking about are ambiguous. They'd be disambiguated using either parentheses, a fraction bar, or by a clear notational definition.
My claim is that in the absence of such a notational definition, in informal contexts, any practicing mathematician would assume that 2x/3y means the same thing as (2x)/(3y), and that 48 "divided by" 2(3+1) means the same thing as 48/(2(3+1))
Nothing he says is false, he just suggests a fraction bar tends to carry the connotation that the following juxtaposed terms in a single-line rendition of the expression would be assumed to be under the bar unless explicitly noted otherwise, which would result in a legitimately ambiguous equation, giving the people arguing that "2" is the correct answer a much more valid argument. He is only saying, simplistically, for his student's sake, that the use of the dividing operator instead of the fraction bar removes any pretense of ambiguity in the following juxtaposed terms, which makes the application of basic order of operations much less convoluted, and therefore there is no reason to assume the entirety of the term is to be considered part of the denominator.
He's basically saying you have to be an idiot to think that you put that whole term in the denominator when there's no fraction bar. He could understand the misinterpretation with more ambiguous notation, but this is very clear-cut.
Now if we're assuming an abelian group...
what i don't get it
Any practicing PROGRAMMER would assume that, because most languages do, just like most languages assume -3^2 = (-3)^2 and not -(3^2) even though technically the second is correct because most people mean the first even though they entered it wrong, just like most people mean (2x)/(2x) when they enter 2x/2x. It is very simply a user-interface facilitation.
Any MATHEMATICIAN will defend the fundamental principles of math to the death.
Even if he's right, this is hardly a fair judgment. I have always been taught that you can assume there are "understood parentheses" around any two juxtaposed symbols for quantities, and that they are to be multiplied. I do not know myself ever to have missed any math exercise by following this rule. I and the many others who make this assumption are hardly "idiots" regardless of whether it turns out this assumption reflects general mathematical practice or not.
Edited by Speusippus#1370 on 6/12/2012 2:30 PM PDT
I will give you guys a hint if you have abcdefg/gfedcba you can just mark all of them out and say it is one... Maybe some of you college professors have forgot about this one...
I think if I saw any student write either of those fuctions I would count off points and mock them.
Edited by Kennyloggins#1272 on 6/12/2012 2:32 PM PDT
Nobody with half a brain would ever present an equation this ambiguously with the attempt to assess your mathematical capabilities. Your teacher, your book, your boss won't write the equation this way, they will write it out as a multi-level expression with a fraction bar and the terms in their correct places. The problem comes from the fact that this is being entered as a single line, which confuses most people when division is involved. The only way you would ever be tested on this is that stupid STAR standardized testing at the end of whatever grade they introduce orders of operations in, and then you don't even know how you did, the school just knows 96% of kids (example) failed it, so they teach harder the next year. It is purposefully deceptive, and no one interested in your education would purposely deceive you.
Notational conventions are directly related to order of operations, which is a fundamental principle of math. A math problem should never have a disputable answer. It can have many answers, infinite answers, but those answers are either right, or wrong. They either fulfill the constraints of the expression following the fundamental principles of math, or they don't. There is no ambiguity. This isn't about whether or not the MLA method is the correct way to site your sources. The rules of math are not open for debate. So yes, this is a discussion about the fundamental principles of math.
did this one already. It is a petty argument on their side at this point.
Technically speaking, yes they are. However, if you wrote either of those two functions in an attempt to convey. (2x2y)/(4x) etc., you will be laughed at. Just add the parenthesis.
Edited by SweetWilly#1217 on 6/12/2012 2:40 PM PDT
True. I said this already above.
Notational conventions are directly related to order of operations, which is a fundamental principle of math.
False. You could create an exactly-as-powerful system of mathematics (and here I mean powerful in the technical sense--validating all the same interpreted formula etc etc) in which the order of operations was completely different. This is because the order of operations is a purely notational matter.
How certain am I of what I just said? EIGHTY FIVE PERCENT CERTAIN!
Edited by Speusippus#1370 on 6/12/2012 2:42 PM PDT
They are the same.
f1(x) = (2*x*2*y*x)/4
f2(x) = (2*x*x*2*y)/4
which are equivalent.
It would even be fair to write it as:
The parenthesis don't matter, and as multiplication is associative, the order in which you multiple doesn't matter. And division is equivalent to multiplying the inverse. So you can do it in any order you want.
See what we're doing?
Mathematics relationships and principles aren't invented, they're discovered. You make basic tools based on real-world application (e.g. addition ; three oranges and three more oranges is six oranges; two groups of three oranges is six oranges total). And the rest of it falls in to place. That's why math is so incredible, and such a beautiful thing.
EDIT: You could change the meaning of symbols, that is true, but the basic idea that the principles of exponents have to be applied before addition and other various operational rules is non-negotiable.
Edited by Mayde#1748 on 6/12/2012 2:47 PM PDT
Whatever, I am leaving this thread because it's not possible to prove something when the disagreeing party is refusing to even listen.
When I asked to perform simple operations on calculator on 2 different equations to see that the results you will get are different I was told:
You can't argue with someone who refuses to even consider different possibility because of being blinded by his own belief.
I am done.
Edited by Grimraven#1853 on 6/12/2012 2:50 PM PDT
People will never learn even with proof. Id like to see you undermine this since its backed by pretty much every university in the world. Also if you even were in a science field in a university this would be used quite often in classes.
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Edited by Gilager#1578 on 6/12/2012 2:57 PM PDT
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