

Subject:
What is 1+1? What is 2^2? I bet Google doesn't know. =D
Category: Science > Math Asked by: raccoonga 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: maniacga on 27 Feb 2005 16:17 PST 
Hello Raccoon, Well, depending on the rules of precedence you use, the result for 2^2 is either 4 [(2^2)] or 4 [(2)^2] The first is the "proper" result according to Dr. Math at http://mathforum.org/library/drmath/view/53194.html and is backed up by a couple different derivations  very interesting reading by the way. If you want an explanation of who "Dr. Math" is, check out http://mathforum.org/dr.math/ and the several links on this page. (its a math Q&A service sponsored by Drexel University) Of course, not every application or programming language follows the "proper" result. Dr Math points out that Microsoft Excel does it the other way as described at http://support.microsoft.com/support/kb/articles/q132/6/86.asp or more concisely at http://support.microsoft.com/kb/q132686/ which notes the "unexpected result", and states it has been implemented this way in all versions of Excel [and perhaps Multiplan before that]. I also thought it was a little humorous that it admits that Lotus 123 does not have this problem.... So  If you really care about the result  add the parenthenses. I certainly do whenever there is ANY uncertainty in the interpretation or result. Search phrase used for this answer: operator precedence math or operator precedence math unary minus exponent for more specific references for a variety of programming languages. Thank you for such a thoughtful question. Maniac PS: If you instead feed (2)^2 into Google, it states... 2^2 = 4 and if you use (2^2) with Google, it states... (2^2) = 4 The right hand side of both are the "correct result" and it illustrates the precedence model used by Google. 

Subject:
Re: What is 1+1? What is 2^2? I bet Google doesn't know. =D
From: justaskscottga 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: windoffirega 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: xcarlxga 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: volterwdga 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: raeyinga 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 indepth 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. 
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