Maths Test! 2(1+2)2/(1+2)

[Terxpahseyton]

I think that something is unambiguous only when everyody agrees on it which is not the case here obviously.

Mathematics is not governed by impressions, or feelings, or the vote. It is governed by laws. And by design, those laws are absolutely unambiguous. If you find a law which is ambiguous, you better get the word spread right a away, because it then would have to be immediately revoked as a mathematical law and who knows what damage it already has caused.

 

[Thorgalaeg]

Mathematical laws are unambiguous, notation is not.

 

[Terxpahseyton]

In this case, mathematical law dictates notation (which as was already noted is, that multiplication and division are on pair priority-wise).

 

[muhtesem insan]

I think that something is unambiguous only when everyody agrees on it which is not the case here obviously.

Everybody who has enough knowledge of mathematics agree on this. Disagreement from people with lack of knowledge does not make it unambiguous.

 

[Thorgalaeg]

Nope, people dictates notation.

 

[Thorgalaeg]

Everybody who has enough knowledge of mathematics agree on this. Disagreement from people with lack of knowledge does not make it unambiguous.

Says who? i already directed you to the IUPAC. Show me similar organism for mathematics and i will stand corrected. Investing yourself with some sort of authority is irrelevant here.

 

[Terxpahseyton]

Nope, people dictates notation.

Yes, in principle, of course. But if you agree that an equation has to be read from left to right, and if you agree that ab means nothing else than a times b, mathematical law takes over. There then simply isn't any ambiguity left. And I would think that we all agree on that.

 

[Thorgalaeg]

You said it yourself: "if we agree". We agree on ab notation but not on 6/2(1+2) notation.

 

[Terxpahseyton]

You don't understand, if we agree on ab (and well left ro right and + and the meaning of brackets and that a/b equals a : b to be precise), the rest logically follows by the law of math. And we do agree on all those accounts I dare to say.

 

[Thorgalaeg]

It would be really interesting (seriously) to see how you develop your rule for the division being first (or second) in 6/2(1+2) starting from ab through mathematical laws without using any convention (of course admiting left ro right and + and the meaning of brackets and that a/b equals a : b)

 

[Hehehe]

I'm sure we can all agree that, if it were 6/2*(1+2), there would be absolutely nothing ambiguous about it. So, it is 2(1+2) that causes the disagreement. That is what we call implied multiplication. There is no rule that states that implied multiplication is given higher priority than normal multiplication, but nevertheless, it is a convention that is sometimes used, and therefore it is an easy mistake to make.

 

[Mise]

What the hell is this thread about?

EDIT: x-post with Hehehe. That pretty much explains it, thanks.

 

[Terxpahseyton]

@Thorgalaeg
Well if ab means the same as a times b, it doesn't matter which one we use.
So our equation reads d/a*b. Which according to mathematical law equals d*(1/a)*b.
So 6*(1/2)*(1+2).
And if we now go from left to right, the answer must be 9 and can not be 1. To assert that the original equation equals 1 would contradict its mathematical correct transformation and hence mathematical law.
@Hehehe
That's what I said on the first page. Though I didn't know that the name was "implied multiplication".

 

[muhtesem insan]

It would be really interesting (seriously) to see how you develop your rule for the division being first (or second) in 6/2(1+2) starting from ab through mathematical laws without using any convention (of course admiting left ro right and + and the meaning of brackets and that a/b equals a : b)

mathematical rules(actually axioms) are determined by the propposer of these. If these axioms are interesting enough matematicians start to use it and it becomes a norm.These axioms for order of operations are used for thousands of years. And all mathematicians agree about this.

 

[warpus]

It's 9

It'd be 1 only if it was written as

6/(2(1+2))

edit: arriving late, didn't read rest of thread, etc.

 

[Leoreth]

Sorry, but first find me any self-respecting mathematician who even uses the division symbol at all. Even if there are strict rules that govern its behaviour it's simply too prone to human error and I've never seen it used outside of the restricted world of computational notations.

The usual algebraic definitions of addition and multiplication even omit the inverse operators completely, simply because they're not necessary. If you already have defined + and *, you can invert +a by adding the additive inverse of a, i.e. +(-a) [note that the "-" here is not the minus operator] and invert *a by multiplying with the multiplicative inverse of a, i.e. *(a^-1) or *(1/a) [the fraction 1 over a].

 

[Mise]

Even the divide sign looks like a fraction: ÷

 

[Thorgalaeg]

@Thorgalaeg
Well if ab means the same as a times b, it doesn't matter which one we use.
So our equation reads d/a*b. Which according to mathematical law equals d*(1/a)*b.
So 6*(1/2)*(1+2).
And if we now go from left to right, the answer must be 9 and can not be 1. To assert that the original equation equals 1 would contradict its mathematical correct transformation and hence mathematical law.

But dont forget what you are using a convention: that the left to right rule is preferent to the multiplication, which is not a problem and universally accepted when you write it as d/a*b. However use d/ab instead of d/a*b and you will see that any scientist understand that as d/(ab) not as (d/a)b. Which reduces it all to a notation problem. For instance, be sincere, if reading a scientific paper you find 3/2x how would you interpret it?

 

[Leoreth]

But dont forget what you are using a convention: that the left to right rule is preferent to the multiplication, which is not a problem and universally accepted when you write it as d/a*b. However use d/ab instead of d/a*b and you will see that any scientist understand that as d/(ab) not as (d/a)b. Which reduces it all to a notation problem. For instance, be sincere, if reading a scientific paper you find 3/2x how would you interpret it?

Your point is of course valid, but frankly I would interpret it as a sign that the author has no idea how to properly use TeX

 

[azzaman333]

6/2(1+2) could reasonably be interpreted as either (6/2)(1+2) or 6/(2(1+2)) depending on the context.