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$2-1+1$; a fairly straightforward question, but I (well, not me, but Henry Reich) found something strange.

Most people would evaluate it as $2+(-1)+1 = 2$; however, this goes against the famed, and fairly standard B.E.D.M.A.S./P.E.D.M.A.S., which states that addition goes first, and then subtraction.

If this is the case, then the answer is $2 - (1 + 1) = 2-2 =0$.

Which is the correct answer, and why is the conventional way (B.E.D.M.A.S./P.E.D.M.A.S.) so ambiguous?

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Cisplatin
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    This is getting ridiculous, answers simply respelling out the same theme. 9 answers? How many ways can you spell "overkill"? – amWhy May 19 '13 at 23:46
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    @amWhy There you go, madness stopped. – Pedro May 19 '13 at 23:50
  • It should be just PEMA: parenthesis, exponents, multiplicative, additive.

    Multiplication and division is in the same group, just as addition and subtraciton.

     – Calmarius Oct 01 '13 at 21:41
  • I dont know how this question attracted so many answers and upvotes for answers... – Lost1 Oct 31 '13 at 18:51

8 Answers8

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This is why those abbreviations are poor. PEMA is a better one for that purpose.

By the way, normally it is PEMDAS (not PEDMAS) and it stands for Parenthesis, Exponentiation, Multiplication and Division, Addition and Subtract. It's just that the "and"s get lost in abbreviation.

Jon Claus
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    Also omitted often "from left to right" for +- and */. – ncmathsadist May 19 '13 at 23:39
  • Indeed, @ncmathsadist! – amWhy May 19 '13 at 23:42
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    In the UK, and I think other commonwealth countries, it’s ?usually (at least, often) taught as BODMAS, with the D definitely before the M (and a B since we call parentheses brackets). Of course, this doesn’t affect the substance of your answer! (Also, I’ve no idea why it’s O instead of E — some googling suggests that orders is/was an alternate name for exponentiation/powers, but I’ve never come across that in any other context.) – Peter LeFanu Lumsdaine May 19 '13 at 23:55
  • In Canada I was taught BEDMAS. (Brackets instead of parentheses, and definitely exponents!) – Lee Sleek May 20 '13 at 01:56
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According to standard algebra rules, $a - b$ parses as $a + (-b)$.

ncmathsadist
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Forget garbage like PEMDAS. Learn mathematics instead.

(And I would take "AS" to mean "addition and subtraction", not "addition, then subtraction". I learned in 6th and 7th grades that those are done from left to right. If someone taught you a rule that addition should precede subtraction in such instances, they are ignorant.)

Michael Hardy
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    I disagree. It's an answer. – Michael Hardy May 19 '13 at 23:45
  • OK, I changed one word. Is that any better? Maybe you should be specific about what you object to. – Michael Hardy May 19 '13 at 23:49
  • @amWhy Oh, let's not get touchy now with "mean" words! – Pedro May 19 '13 at 23:53
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    I consider the text in parentheses an answer, though it was already posted by Jon Claus. – anon May 19 '13 at 23:53
  • @amWhy : The "first comment" was not intended to please anyone. I'd never have guessed that you thought it was if you hadn't said so. The rules for which "PEMDAS" attempts to serve as a mnemonic are not written in stone, but there are reasons for them. Understanding those reasons would be a far better aid to memory than childish mnemonics like "PEMDAS". – Michael Hardy May 20 '13 at 00:20
  • Michael, I think my frustration with the thread, as a whole, got the better of me. It was wrong to single you out. And indeed, your comment which follows is precisely the logic I used in my answer to the so-called duplicate, which was to confirm the OP's response to notes he read. I would have upvoted any comment you might have made regarding this. So I'm entirely sympathetic to your answer. I apologize for suggesting you were "pandering." That's a loaded word, and was ill-chosen word for me to have used in this context. – amWhy May 20 '13 at 00:29
  • To be honest, I only learned of "PEMDAS" and BODMAS here at Math.SE. I learned as you learned, without resorting to mnemonics. – amWhy May 20 '13 at 00:35
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If you're taking the minus sign out:

2 - (1-1) = 2.

I think you're misunderstanding BEDMAS. You can always make it all addition if you'd like?

2 + (-1) + 1 = 2.

Islands
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Multiplication and division can be performed in any order, and the same holds for addition and subtraction. I learned it as PEMDAS, to drive the first point home. I suspect the only reason that addition always precedes subtraction in the mnemonic is that it makes the acronym simpler to say.

Cameron Buie
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The usual convention is to read $a-b$ as an abbreviation for $a+(-b)$, that is, "add the opposite".

This makes possible to associate or permute the terms in the expression getting always the same result: $$ 2-1+1=(2-1)+1=2+(-1+1)= 2-1+1=2+1-1=-1+2+1=1-1+2 $$ This should explain why this convention is used instead of a more difficult one. Just forget about subtraction, which has less pleasant properties than addition.

The same is for "division": we avoid it preferring "multiplying by the inverse". This avoids ambiguities.

How would you parse $$ 3-1+2-3+4 $$ with Henry Reich's convention? With the standard convention it is $$ 3+(-1)+2+(-3)+4=5 $$ That's all: mathematics is based on conventions.

egreg
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Think of each number as an item; $2−1+1$ evaluates to: $$(+2)+(-1)+(+1)$$ Thus, represented in succession, it evaluates to:

$$n = 0$$ $$n = n+2 = +2$$ $$n = n-1 = +1$$ $$n = n+1 = +2$$ $$n = 2$$

JohnWO
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    And by the rules of transitivity, $0=1=2$, and almost all math is wrong. This makes sense if you're in comp-sci, of course. – Cameron Buie May 20 '13 at 03:21
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Take it like a succesion, $$2+(-1)+1=2$$ first $$2+(-1)=1$$ then $$1+1=2$$ like this $$2+(-1)+1=2$$ $$2-1+1=2$$ $$2=2$$

JgMc
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