What is $2 - 1 + 1$?

Question

$2-1+1$; 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?

Answer 1

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.

Answer 2

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.

Answer 3

According to standard algebra rules, $a - b$ parses as $a + (-b)$.

Answer 4

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.

Answer 5

Take it like a succesion, $$2+(-1)+1=2$$ first $$2+(-1)=1$$ then $$1+1=2$$ like this $$2+(-1)+1=2$$ $$2-1+1=2$$ $$2=2$$

Answer 6

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.)

Answer 7

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.

Answer 8

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

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