Are the rules of math arbitrary?

Question

It seems to me that unless an answer is ALREADY known (by whomever has the answer the way THEY DID IT) the order of operations are arbitrary. There certainly are times when the rules make sense, and other times they seem completely whatever some jackass 3000 years ago made up. Switch the order of operations around in an expression (not equation) and you can get all sorts of answers or simplifications. Math is only a perfect language insofar as long as everyone follows the rules! Or am I crazy??

Answer 1

The order or operations is *not* arbitrary. Multiplication is a short form for repeated addition of the same number, so its precidence is above addition; otherwise, the repeated additions wouldn't be evaluated correctly.

Similarly, exponent form is repeated multiplication of the same number, so its precidence is above multiplication.

Parentheses, by their nature, need to be evaluated before anything outside of them are performed, so they have precidence above everything else.

So we have: Parentheses, Exponents, Multiplication, and Addition. Since Division and Subtraction are simply the opposites of Multiplication and Addition, their precidence is the same as theirs.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction is then the final basic order of operation.

Answer 2

I don't think your question is really about math. Take the same argument you're making and apply it to grammar. the "expression", here a phrase, must follow the rules of grammar to make sense. If I took words (like numbers) and put them in order according to different rules, such as alphabetical, the same phrase would be totally different. The rules that you're arguing against seem more like rules of coherence. The underlying mathematical concepts do not change and are not arbitrary. Imagine you are adding 3 to 4, and then multiplying by 2. Simply: 3+4=7 7*2=14 The rules you are having trouble with are the rules that allow us to apply grammar to math... (3+4)*2=14 What you are saying is that, if I used different rules, I could say... 3+4*2=11 But this change affects the rules of "math grammar", rather than the underlying concepts of math. So, in conclusion, the rules you mean are completely arbitrary, but these rules are more concerned with coherence than mathematical concepts. Hope that helps.

Answer 3

You have laws then you have theorems: Laws are always right and used in engineering. Theorems on the other are expressions which are supposedly right around 90-99% of the time. For that reason they are not used in engineering.

That for example the Golden Gate Bridge. When they started building it they started on both sides of the bay and met in the middle. Ok! if they did their calculations using theorems what would have happened if that had been the 1% the expression was wrong and they ended up twenty; thirty feet off when they met in the middle?
That's why I opted of engineering Algebra, Trig and Calculus. If it wasn't a law we didn't fool with it. Theorems are no good in engineering math. You have to be sure not 99% sure! You have to be 100% sure.

Answer 4

Um...it's math. Yes, the rules must be followed for everyone to have consistent answers. Yes someone made it up to model reality. Yes, it is about as exact a science as we (humans) have. No, you can't mess with it, but if you're extra bright you can stand on the shoulders of Giants and model something new.

Answer 5

No they are NOT. For example, if you were given a problem with addition, multiplication and division, you are to do certain things in a certain order, or yoiu will get the WRONG ANSWER.

Answer 6

i know !!

u r sooo not crazy i mean they shouldnt change the math rules often rite??