Is Bodmas a convention or a fundamental feature of mathematics?

[jake-the-peg]

One of the regular "order of operations" questions came up in How it works the other day and this thought struck me.

Why is the order of operations the way it is? Is it just a general convention or is there a subtle underlying reason for it?

Would the world be different if everybody decided that 3+6/3 was 3 rather than 4?

Would planes fall out of the sky if engineered under this assumption? is this truely fundamental or just a convention?

[jake-the-peg]

Maths by its very nature must be internally consistant

Ah what a nice if somewhat 19th century idea

Russel and Whitehead spent many many years trying to formulate maths on the basis of pure logic - they even published a huge tome famously proving that 1+1=2 after several hundred pages.

Alas they didn't count on Godel coming along and showing that some Mathematical ideas simply couldn't be proved.

Turing came along and made matters worse by showing that you couldn't know whether the problem you were working on was one of them! (he did more than just computers!)

Consequently you can never prove that a whole load of Mathematical systems are actually internally consistant

[vascop]

Jake
Your last post has nothing to do with your original post! Please stick to the original point.

[beso]

Curiously. When I first learnt maths in Queensland Australia in the 1960s we were told it was BOMDAS.

It actually makes no difference mathematically and I always thought it was a nicer word.

[beso]

When I bought my first calculator in 1975, one of the the tests was to check for BOMDAS compliance. Some passed some didn't. I bought a Sanyo which applied the convention.

This question is entirely about convention of expression and no deep mathematical principles are evoked because it is irrelevant to the maths.

I write computer programs. The languages use vast numbers of shortcut notations to simplify expressions. It I had to always type the full reference to every object in my program I would go mad.

Having to include explicit brackets for every expression because someone eschews bomdas is not only tedious to write but tedious to read as a programmer.

[chakka35]

vascop, of course the example you give equals five. If the answer 3 were required it would be written 3+6 'all over' 3. (sorry, but I can't denote that without messing about). Your example is not ambiguous at all.

But the example given in How it Works was: 2 + 2(2+2) x2, which is ambiguous. The final x2 is floating, which is why you get two equally defensible answers - which means that the original formulation was invalid. Maths - even its simplest manifestation, arithmetic - is meant to be precise.

[factor-fiction]

Chakka- the original formulation 2 + 2(2+2) x2 was NOT invalid, because there is a convention (BODMAS) for setting out and performing these calculations. You may prefer to set it out differently (and I prefer to use brackets in case someone misapplies BODMAS) but it isn't wrong. The question probably arose in a text book in a lesson on 'order of operations'. No marks would be gained for saying INVALID FORMULATION

[THECORBYLOON]

BODMAS is a convention in the same way that it is convention that a-b means subtract the value of "b" from "a" and not vice versa. In the same manner, dog bites man, by convention in the English language, means the man was bitten by the dog and not vice versa. The meaning in both examples is changef if the convention is reversed but either way, it is important to know what the convention is.

[sarahparry88]

Addition and multiplications are both commutative and associative
So taking BODMAS
2 + 3 x 4 = 2+(3 x 4)
We want this to be the same as
2 +( 4 x 3)
(4 x 3) + 2
(3 x 4) + 2
which it is so the laws of associativity and commutativity hold.
However, if we take it left to right
2 + 3 x 4 = (2 + 3) x 4
We would like this to equal
(3 + 2) x 4
4 x (2 + 3)
4 x (3 + 2)
But using the same convention reading left to right
2 + 3 x 4 = 20
3 + 2 x 4 = 20
4 x 2 + 3 = 11
4 x 3 + 2 =14
So I'm pretty sure it is just a convention, but for the laws of associativity and commutativity of multiplication and addition to hold it is the only way to make sense of an otherwise ambiguous expression.