Can you do this simple maths problem?

[Roller123]

There is no trick...

Again, everything done to the equation must be provable. You said "But the precedence of multiplication and division are the same. Obviously if an operator is associative it doesn't matter which order you evaluate. If it isn't associative you evaluate from left to right"

"But", "obviously" and "if" are not proofs. These are opinions, i will dont discuss their validity, since thats not the point here. The point is, how did you come to the conclusion that the equation is not associative. And even more, must be done from left to right.

 

[ParadigmShifter]

It's just a convention. You can't prove it is correct, since the other way is just as valid.

 

[Roller123]

You cant prove its not associative?

 

[ParadigmShifter]

Probably.

(ab)^-1 = b^-1a^-1

Otherwise multiplicative inverses wouldn't work correctly.

EDIT: There's a real maths thread in sci/tech btw

 

[Bill3000]

You cant prove its not associative?

Can you prove that the glyph 1 represents the number 1?

 

[Earthling]

The correct answer, following what standards do exist for poorly written situations like this, as provided by international professional organizations and countless published texts, is 2. Also explained in other threads here, didn't really need a new thread on this.

 

[ParadigmShifter]

That would be cool if it wasn't wrong (the answer is 288).

 

[Earthling]

No, the correct answer is 2. 288 results from using the wrong order of operations. Multiplication by juxtaposition takes precedence over other operations. Though if you have a published text or statement by a professional organization on hand showing otherwise it would be great to see it. As this has already been all over the Internet it's doubtful, nobody else anywhere apparently found a single valid example which is saying something, but nothing against you trying. However the overwhelming preponderence of evidence everywhere has shown the more accepted convention would yield 2.

 

[ParadigmShifter]

No it doesn't.

Multiplication and divison have the same (left to right) precedence.

Hence google, and wolfram alpha giving the correct answer. Wolfram doesn't mess around, it is based on mathematica.

 

[Perfection]

The answer is to give the maker of the statement a chewing out.

 

[ParadigmShifter]

Of course, I said that in my first post (dodgy lack of brackets to make it deliberately confusing).

I forgot to say in my last post that left to right precedence (and precedence of operators in general) is arbitrary, but we have rules and we must stick to them, otherwise confusion abounds.

 

[Roller123]

EDIT: There's a real maths thread in sci/tech btw

No thanks, but what im saying is that basic proofs are easily taken to be self-explanatory. Its pretty anal, but it must be, lol. If associativity is proven, any further steps can be ignored since it becomes trivial to solve. Thus discussing order is only a second step. Which, since its not defined in the first post, can go either way, thus 2 and 288 are both valid answers.

 

[Earthling]

Yes, it does equal 2. Though please, find a single published text or scholarly work using this notation otherwise. What really impressed me again on this issue elsewhere on the net was that not a single person found a single one in thousands of possible attempts. (versus the thousands that were found with the same convention holding that 2 is the correct answer). For example, the AMS convention:

We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division. For example, your TeX-coded display $${1\over{2\pi i}}\int_\Gamma {f(t)\over (t-z)}dt$$ is likely to be converted to $(1/2\pi i)\int_\Gamma f(t)(t-z)^{-1}dt$ in our production process.

*ie. 1/2π = 1/(2&#960*
Wolfram gives the correct answer below, but that's a fallacy for anyone to argue on either way since computer tools aren't perfect and everyone knows this. And there's documented evidence of different programs yielding different results (MATLAB, Microsoft Excel, etc... give 2, for instance, after correcting for parsing errors entering the formula)

http://www.wolframalpha.com/input/?i=48/2x,+x+=12

For fun you should check this out too, see if you agree...

http://www.wolframalpha.com/input/?i=sin+2pi

 

[ParadigmShifter]

1/2pi is pi/2, that's much more useful than 1/(2pi).

1/(sqrt(2pi)) is pretty handy though, but sqrt has a higher precedence than division anyway

You should put arguments to sin in brackets anyway...

 

[Earthling]

1/2pi is pi/2, that's much more useful than 1/(2pi).

Well, you could intepret it that way, but you'd generally be wrong. Obviously as others have said this is a matter of conventions, except the one you think is more acceptable happens to be the one never used by any publisher, journal, or professional organization.

You should put arguments to sin in brackets anyway

And yes, obviously, just like one should put brackets correctly in the equation in the OP. The point being that computer tools or calculators will interpet things incorrectly or differently, and it's bad form all around to suggest they make for acceptable conventions.

 

[Roller123]

People, this is a troll question. Ask a badly defined "math"/"physics" question and let people battle over it based on their interpretation on what the input parameters actually are until their heads explode. Its not even a good one. Here is a much better one:

The case of the plane and conveyor belt:

A plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the wheel rotation speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?"

(my answer: it will not take off)

 

[ParadigmShifter]

The standard mathematical precedence rules are what is acceptable.

Publications can use a long line if they want to be unambiguous (see my code block snippet earlier).

This is really a non-argument. I am correct

 

[Earthling]

And the standard precedence rules say the answer is 2. Back to the same circle again. Though I am correct.

Yes, Roller, everyone realizes that. Still, can't hurt to make people aware of the problems of poor notation in general. And even more fun this one did seem like a neat social experiment. Elsewhere on the net when this came out there would be vastly skewed results on different sites (see, it sucks the OP here didn't make a poll) kinda resulting from a chaos-theory like snowball effect - once one side got more popular more people would jump in to vote for the "right" answer and troll just for the sake of it. There were always about four sides though, people on either side arguing the other side was just taught wrong when they were 8 years old, this was funny for groupings like Chinese/Indians versus Europeans and whatever, complete trolls obviously, and then people who can cite actual published guidelines, texts, etc... The latter is really why the better answer is 2, you'll never see in any publication anywhere, ever, an expression like the one in the OP to mean 288. But PV/RT = PV/(RT), E/kt = E/(kt), 1/sC = 1/(sC) and countless other examples of in-line text just like what we see here. It's as much of an accepted convention as you can get with something like this.

 

[Roller123]

Saying that the answer is 2 is just as bad as saying it is 288. Its just undefined, due to insufficient parameters. Ask the OP which way he wants it to be solved, and we have our answer.

 

[ParadigmShifter]

No it isn't.

Operator precedence is well defined in mathematics.

EDIT: The problem is, mathematics has more than a single line of ascii to play with.