Poll: 6÷2(1+2)

[gambitt]

you've already made an assumption of 2(x^2)

the question was

Explain why 2x^2 is read as 2(x^2) rather than (2x)^2 other than simply by convention.

Without convention this could be read as 2x * 2x or 2*x*x

You *know* that it is 2(x^2) however you only know that it is due to convention. If that convention didn't exist then you could argue that it is ambiguous as people are attempting to do within this thread.

Let's work backwards:

(2x)² = 4*x*x [basic expansion - if you don't follow this part you don't understand basic multiplication]

4*x*x = 4*x² = 4x²

now for 2(x²):

2(x²) = 2*(x*x) = 2*x*x = 2x²

2x² != 4x² therefore the 2nd one is correct

Perhaps you're getting confused between convention and simple notation

 

[dowie]

Let's work backwards:

(2x)² = 4*x*x [basic expansion - if you don't follow this part you don't understand basic multiplication]

4*x*x = 4*x² = 4x² no if the convention was that 2x² is equivalent to (2x)² then your answer to the basic expansion would have to be written 4(x²) which is indeed equal to (2x)²

now for 2(x²):

2(x²) = 2*(x*x) = 2*x*x = 2x² yes this is the convention we use

I'm quite amazed that you don't actually realise you're following a convention here...

 

[gambitt]

Anyway, I think we've broken this down as far as we can.

We've established that you take this "left to right rule" as gospel, whereas I consider it a convenient way for lazy programmers to avoid compiler errors when using sloppy notation.

I'm off to enjoy what's left of this nice day

 

[gambitt]

I'm quite amazed that you don't actually realise you're following a convention here...

You've gone into ultra pedantic mode - not really surprising given that you skipped over the more difficult questions I sent your way.

 

[dowie]

You've gone into ultra pedantic mode

Yes and you have seemingly forgotten that when evaluating stuff you take for granted you are actually following convention. Without convention you'd need parenthesis everywhere.

 

[silversurfer]

{(Yes) (and) (you have seemingly forgotten) (that) (when evaluating stuff you take for granted) (you are actually following) (convention). (Without convention) (you'd need) (parenthesis) everywhere(.)}

 

[gambitt]

And I'm back in again

no if the convention was that 2x² is equivalent to (2x)² then your answer to the basic expansion would have to be written 4(x²) which is indeed equal to (2x)²

Because 4x² = 2²x² which is clearly not the same as 2x² - this is BASIC NOTATION - I know you want me to say "because BODMAS says so!" but what I've just done is broken down each expression into it's simplist form and compared the results of each. This is what we call proof which is how convention is made. Convention isn't just made up, it is built from first principals.

Now that I've had a go at answering your sidetracked question, how about you have a go at this one:

Or how about about addressing the fact that different programming languages use different associatve precedences thus give different answers? I note that you gave that one the slopey shouder treatment as well.

No? Still want to just dodge the difficult questions and go for the circular straw man argument about general convention option instead? I could see why you'd want to.

 

[ordinaryjoe]

Everything can be proved from first principals, so where did this "left to right convention" come from? Why does it have to be used at all? Can you find any information about it other than some primary school examples?

Let me guess "err... you're sidetracking the thread"

In my MEng Aerospace Engineering degree, I got a question wrong for doing division before multiplication when the multiplication was on the left.
The so called 'primary school left to right rule' is used in degree level maths
24÷3÷2 for example highlights the point. What would you evaluate the answer to be? Without the left to right rule, you could easily get 16.

 

[ordinaryjoe]

Because x² = x*x so 2x² = 2*x*x not 4*x*x

And how do you know to do the 2*x before doing the indice other than by bodmas?

 

[ordinaryjoe]

Let's work backwards:

(2x)² = 4*x*x [basic expansion - if you don't follow this part you don't understand basic multiplication]

4*x*x = 4*x² = 4x²

now for 2(x²):

2(x²) = 2*(x*x) = 2*x*x = 2x²

2x² != 4x² therefore the 2nd one is correct

Perhaps you're getting confused between convention and simple notation

So how do you know that the 2nd one is correct, and not the first one? (other than by convention/bodmas)

 

[gambitt]

So how do you know that the 2nd one is correct, and not the first one? (other than by convention/bodmas)

Jesus wept.

The question was explain why 2x² is read as 2(x²) rather than (2x)².

I took each expression in turn and broke it down. First (2x)² which yielded 4x² followed by 2(x²) which yielded 2x², which is what he was looking for. Therefore 2(x²)=2x² !=(2x)² I put it in red so you can see the answer is in the question.

What's next - asking me to prove that 1 = 1*1 and then moaning when I can't break it down further? How about addressing some of my questions for once rather than continuing down this side track?

 

[Pinkribbonscars]

Yes and you have seemingly forgotten that when evaluating stuff you take for granted you are actually following convention. Without convention you'd need parenthesis everywhere.

The question in the OP isn't written conventionally though.

 

[Pinkribbonscars]

In my MEng Aerospace Engineering degree, I got a question wrong for doing division before multiplication when the multiplication was on the left.
The so called 'primary school left to right rule' is used in degree level maths
24÷3÷2 for example highlights the point. What would you evaluate the answer to be? Without the left to right rule, you could easily get 16.

I find it hard to believe you were given a question where you needed to use the 'left to right rule'.

24÷3÷2 would never be written by anyone semi-numerate.

 

[QlimaxUK]

WOW thread has exploded is there going be a lot of murders in the news next week between ocuk members over this thread

 

[Shayper]

Is this still going?

*Sigh*

 

[dowie]

Because 4x² = 2²x² which is clearly not the same as 2x² - this is BASIC NOTATION

Yes indeed it is basic notation

and the reason we don't need to write 2(x²) is because we have convention....

Without and order of operations 2x² could be interpreted as 2(x²) or (2x)²

we follow the convention that 2x² means 2(x²)

 

[gambitt]

Yes indeed it is basic notation

and the reason we don't need to write 2(x²) is because we have convention....

Without and order of operations 2x² could be interpreted as 2(x²) or (2x)²

we follow the convention that 2x² means 2(x²)

Convention is created by testing proofs from first principals to see what holds true. Rules are formed in the cases where the notation holds (otherwise known as convention) which is what I've done above (albeit in a rather less detailed manner).

You are blindly following it without even knowing how it is formed or where it comes from. There isn't some maths bible somewhere that states "THESE ARE THE LAWS OF MATHS AND MUST ALWAYS BE OBEYED". They were created from the simplist form of mathematics, then some smart people took those principals and created more complicated conventions and so on...

ONCE AGAIN you have skipped over ALL of the questions I have asked you. Why is this?

 

[dowie]

The question in the OP isn't written conventionally though.

Yes and no one is saying it isn't a silly question - it still doesn't stop you from using convention to get an answer. If we didn't have any conventions for operators then we'd need parenthesis everywhere.

2x² is 2(x²) not (2x)²

everyone knows this but we only know this because conventionally that is what we mean by 2x²

 

[dowie]

ONCE AGAIN you have skipped over ALL of the questions I have asked you. Why is this?

Because I've got better things to do than entertain someone who doesn't really know what they're talking about and is trying to sidetrack the thread.

 

[gambitt]

Because I've got better things to do than entertain someone who doesn't really know what they're talking about and is trying to sidetrack the thread.

Says the guy who's been banging on about convention for 2x^2 for the past 10 posts but won't (can't) address the convention applied to a basic integral

You mentioned calculators and programming earlier in the thread - why won't you answer the question about different languages using different conventions?