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I've problems with that BODMAS rule. I lost my 5 marks in the test for that. Why we should follow that DMAS rule? Why it is not any other combination? Are there any derivations for it? PS:-Sorry I'm confused with the tags with this question. I don't need any easy way to remember it.

  • One might simply use parentheses throughout to avoid ambiguity. So what we write as $a+b-c\cdot d+e$ would be written $((a+b)-(c\cdot d))+e$. This looks awful and is even harder to read in spite of it being theoretically more precise. It is rather a matter of convention why we agree to drop many of the parentheses. By any such convention, at most one of $(a+b)\cdot c$ and $a+(b\cdot c)$ can get rid of its parentheses. And as is the general case with conventions, the most important part is to agree on it. (There are things that speak in favour of the convention actually picked, though) – Hagen von Eitzen Apr 09 '17 at 11:02
  • I want to know why DMAS is followed, why it can't be SAMD? –  Apr 09 '17 at 11:03
  • Just because it makes writing a bit easier,other then that it's just because one convention had to be chosen and BODMAS seemed the best. – kingW3 Apr 09 '17 at 11:05
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    @AbhasKumarSinha: See the above duplicate. It addition/subtraction bound tighter, we couldn't write polynomials without parenteses. Since we have $a(b+c)=(ab)+(ac)$ but not $(ab)+c = (a+c)(b+c)$, doing MD before AS means that anything that does need parentheses can be rewritten into something that doesn't, at the cost of duplicating some subexpressions. – hmakholm left over Monica Apr 09 '17 at 11:06
  • Actually, I've a question, using dmas changes everything for ex- 1+2/2 = 3/2, but, why use DMAS here and change it into 2. There is a difference of 0.5 between correct value and incorrect value. –  Apr 09 '17 at 11:09
  • It's the convention. Why the convention is such, the reasons might be that people felt multiplication and division fused the numbers together more, being kind of stronger operations and therefore take priority. – Heimdall Apr 09 '17 at 11:10
  • But @Heimdall as far I know, Mathematics is a subjects where proofs have meanings rather than assumptions. There must be a reason behind it. –  Apr 09 '17 at 11:12
  • P.S. These acronyms may be confusing, e.g. they end with AS, so they may suggest to some that addition is done before subtraction. Won't work with 5-4+3, though. – Heimdall Apr 09 '17 at 11:13
  • @Heimdall why Additions before Subtractions? –  Apr 09 '17 at 11:15
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    @AbhasKumarSinha: Addition and subtraction have the same priority. The only reason the mnemonic has the A before the S is because it can't have the letters on top of each other -- $\rm {}^B_P O {}^M_D {}^A_S$ would not be convenient to pronounce. As Heimdall says, using an acronym in the first place is probably a bad idea -- it is much better to remember the reason why the convention is as it is. – hmakholm left over Monica Apr 09 '17 at 11:18
  • Why do you drive on the left of the road? Could you drive on the right? Either would work as long as everyone agrees.

    There are alternatives but they are not very common or popular. Have a look at Polish Notation. It avoids precedence rules and parentheses.

    https://en.wikipedia.org/wiki/Polish_notation

    There is a variant called Reverse Polish Notation. It was popular with some very early electronic calculators.

    https://en.wikipedia.org/wiki/Reverse_Polish_notation

     – badjohn Apr 09 '17 at 11:18
  • @abhas This is not about reasoning, it's about language. In order to formulate statements, whether they are axioms or theorems, you need a language in which to formulate statements. A part of that language is expressions. By all means, write an article using different language, where in expressions the four basic operations have different priorities, but as it will be an unconventional language, you'll need to clarify in your article what language you're using. – Heimdall Apr 09 '17 at 11:20
  • @badjohn okay, it does't changes the mathematical value, but why Multiplication and Division before Addition and Subtraction? –  Apr 09 '17 at 11:22
  • @AbhasKumarSinha It would change how we wrote maths but I don't see that it would change the value of the maths. Or, do you mean that it would change the value of a particular expression? ASMD would change $2 + 3 \times 4$ from 14 to 20. Well, we would have to change what we wrote. With the current conventions, the parentheses can be dropped from $2 + (3 \times 4)$ but not from $(2 + 3) \times 4$. That would reverse if we changed to ASMD. As I said, it is like the driving rule: either would work but we need to agree. Most mathematicians have agreed on M and D before A and S. – badjohn Apr 09 '17 at 11:28
  • @badjohn but, who decided that we've to use DMAS not ASMD? Why he thought DMAS is correct? –  Apr 09 '17 at 11:36
  • @AbhasKumarSinha Addition before subtraction because there's A before S. I know that's not the rule, that A and S have the same priority and that they are done left to right. – Heimdall Apr 09 '17 at 11:39
  • @AbhasKumarSinha I don't know and I am not sure whether anyone knows; it might be lost in history. Actually, it is not quite as arbitrary as the side of the road. As others have explained, polynomials are simpler with the current convention. Try taking lots of common formula and rewriting them as ASMD. Some will get simpler but others will get more complicated. My guess is that on balance it will be more complicated. Remember the Polish Notation that I mentioned; other proposals have been made. – badjohn Apr 09 '17 at 11:40
  • Oh! Thanks, I've got it, but last if changing the combination of AS and MD, how we can decide that which one results in correct value DMAS or ASMD? as you took the example of 2 + 3 x 4, How we can conclude which is correct Value 14 or 20 MATHEMATICALLY? –  Apr 09 '17 at 11:43
  • @AbhasKumarSinha There is no mathematical way to be sure whether $2 + 3 \times 4$ is $14$ or $20$. Either you trust that the author is following the conventions, you ask them (if possible), or you proceed with caution because you don't trust them. I think that in any serious maths today (and quite far back), you are unlikely to find $2 + 3 \times 4 = 20$. However, it might be likely with amateurs. For example, there are often endless discussions on Facebook on the subject. – badjohn Apr 09 '17 at 11:55
  • @AbhasKumarSinha We can't. It depends on the language used. The conventional language is such that 2+3×4 means 2+(3×4) and not (2+3)×4. In the language where priorities are the other way around the distribution law would look like a×b+c = (a×b)+(a×c). It's up to you which language you use, but when talking to one another both (all) need to use the same language otherwise we won't understand one another. – Heimdall Apr 09 '17 at 11:55

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