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Assumptions are open to interpretation, therefore not specifying the order isn't a valid method other than in general math.
And no, I ain't going to try remembering all the equation theory just to prove this point.
don't wanna be argumentative, but...
Yes it was the first link from google.
I don't get the relevance of your link, there's not a single calculation on that page where adding removing or moving brackets (or whatever the technical name for them is) would make any difference to the answer.
However, on the calculator on the next page http://www.angelfire.com/pa/baconbacon/page3.html it doesn't matter what order you enter the equation in, if you don't add any brackets it always gives the answer 6.
If you note on that page, there is not one place where it is assumed you will interpret by any general rule how the calculation is done. It is implicitly specified. Implying leads to errors. If one does not wish for a calculation, or anything else for that matter, to be interpreted, then implicit specification is required. If it is not, it is open to interpretation.
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