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Q: What is 1+1? What is -2^2? I bet Google doesn't know. =D ( Answered,   5 Comments )
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 Subject: What is 1+1? What is -2^2? I bet Google doesn't know. =D Category: Science > Math Asked by: raccoon-ga List Price: \$2.42 Posted: 26 Feb 2005 21:45 PST Expires: 28 Mar 2005 21:45 PST Question ID: 481638
 Ok. So 1+1 is 2. But -2^2 is 4? That's what Google Says. But is it so? [ ://www.google.com/search?q=-2^2 ] For the sake of fun (and my \$2.42) I would like to hear what you (Google Researcher) might like to say about this before I elaborate with my own findings. It has been a heavily argued topic today, so I'm looking for a fresh opinion. Thanks. I would like an answer from someone taking a Math major or who has a degree in Math, please.
 Subject: Re: What is 1+1? What is -2^2? I bet Google doesn't know. =D Answered By: maniac-ga on 27 Feb 2005 16:17 PST
 Subject: Re: What is 1+1? What is -2^2? I bet Google doesn't know. =D From: justaskscott-ga on 27 Feb 2005 11:53 PST
 I don't see a problem. A negative times a negative (a negative squared) is always a positive. It would be a problem if Google said -2^3=8. But it gets that right too -- the answer is -8. -2^3 Google ://www.google.com/search?hl=en&lr=&q=-2%5E3&btnG=Search (I would answer the question, with citations to reputable web sites, except that I don't have the credentials you mention.)
 Subject: Re: What is 1+1? What is -2^2? I bet Google doesn't know. =D From: windoffire-ga on 27 Feb 2005 15:12 PST
 Clever Clever, raccoon. Please Excuse My Dear Aunt Sally. That phrase is an acronym to the Order of Operations in Mathematics: (), exponents, multiplication, division, addition, subtraction. (Yes, multiplication and division are equal, as are addition and subtraction, but lets be kind to the acronym.) Example: 2+2*3 doesn't equal 12, but rather equals 8, since the 2 and 3 are multiplied first. It would equal 12 if the problem was given thusly: 2+(2*3). Therefore, going back to the original problem we can see that -2^2 means -(2^2), which goes to -(4), or -4. Therefore Google does have a bit of code correction to do. (Sorry Justaskscott)
 Subject: Re: What is 1+1? What is -2^2? I bet Google doesn't know. =D From: xcarlx-ga on 27 Feb 2005 17:55 PST
 I am not the credentialed person you requested either, but I put out the following for discussion: First, order of operations says to do multiplication before subtraction. The application in this case could be argued if someone thinks the exponent is a special case, or if they think a negative superscript is a special case. But consider this... The negative must not be permanantly attached to the number because that would invalidate the simplification method of swapping/canceling negatives. Pretend the plus/minus signs that are directly next to the numbers are superscript and the ones seperated with a space are regular operations: 1 - -1 is equal to 1 + +1 But what about "1 - -2^2" ? ...simplified to: 1 + 2^2 we get 5. This MUST be correct, or else we can no longer do a lot of math that we have been doing for many years. But if we keep 1 - -2^2 and follow the rule of Google, we get 1 - 4 = -3 We could make a rule that we can't cancel/swap +/- to simplify exponents in addition to the rule that says we can in other cases. But it would be the only time a multiplication unit was "weaker" than the surrounding add/subtract operations, and it would make life more complicated to have two rules rather than one just because our first impression of the number was a particular (and wrong) way. It is far more logical to say that if you want to square the whole thing you must say (-2)^2 than to make exceptions for the order of operations and positive/negative simplification.
 Subject: Re: What is 1+1? What is -2^2? I bet Google doesn't know. =D From: volterwd-ga on 08 Mar 2005 07:40 PST
 Forget googles rule... -2^2 is -4... didnt you pay attention in grade school? power takes precedene
 Subject: Re: What is 1+1? What is -2^2? I bet Google doesn't know. =D From: raeyin-ga on 16 Jun 2005 16:01 PDT
 Maniac's right. The statement is ambiguous. Like Dr. Math, sophisticated treatments of the subject would probably say that the exponent comes first, then the negative. However, this is *not* the same as the rules you learned in grade school. They didn't cover this issue because it's not a big deal when you're writing exponents as a superscript. Introducing the carat, or the term exp, creates a whole new issue in matters of precedence. In other words, I think you're assuming that the ^ (or the term exp) should be treated the same way as a superscript. Don't get me wrong, I really think that an in-depth analysis would show that it is best to do exponential functions first. However, computer programmers, and hence computer programs, do not all agree with me. Just use parentheses.