Quote:
Originally Posted by winders
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Scott, in all the links the authors are merely expressing the idea that not all readers have learned or use the mathematically correct interpretation of common expressions, not that there isn't a common inviolate set of rules.
If you study math at a deeper level than is common is HS or even undergraduate math the reasons become more obvious. There are symmetry, associative, commutative, distributive, identity and inverse axioms that make up the mathematical concept of a Field which includes a group of #s in this case Real #s, The Field Axioms define what can be done on a given set of data and in what order. You need to understand the rules for the data set and the field axioms that apply to the data set. It is boiled down to overly simplified mnemonics in HS and undergrad work. This is generally adequate for most purposes but can fail at surprising places to those that haven't fully integrated all of the rules, both the obvious overt ones and more subtle underlying ones..
Wong, in the second link notes that simplicity of presentation often precludes including all of the parentheses that would eliminate all of the ambiguity. He goes on to urge clear unambiguous notation. This is what all good math teachers do, and what many less gifted math teachers don't do and what causes no end of difficulty for students(and teachers) who know most but not all the rules. In the absence of parentheses there are rules that tell the solver what to do and in what order, some obviously don't know or don't follow them.
The fault in the original question was w/ the teacher he/she intended something other than what she wrote, and then compounded the fault by not acknowledging the mistake.