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Originally Posted by winders
Bill,
Yes, I understand all of that. The issue is that the difference between the layman and the high level academic is huge. Also, conventions change over time as mathematics evolves. Regardless, what I said is true. The conventions are not set in stone. The math itself is inviolable, but the way we write it down and interpret that writing is not. aigel is putting to much faith in the conventions being absolute and not ambiguous.
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The issue is that the difference between the layman and the high level academic is huge
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Yes but it all comes down to either knowing and following all the rules or not, in this thread there is no higher level esoterica involved
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conventions change over time as mathematics evolves
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there is and has been evolution but as far as the HS math discussed here
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the way we write it down and interpret that writing is not
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again the HS math discussed here is well defined and not subject to debate except by those that haven't fully integrated it.
It is true that other countries have different notations, these are entirely process/organization oriented and not presentation oriented(by that I mean the way they show things like the process of long division or manually calculating a root). They would evaluate the expression here using the same rules as us.
Bottom line is the teacher erred and wouldn't own up to it. It wasn't a matter of ambiguity except in his/her own mind. In every one of the controversial math questions i've seen here and at my job the error has always been that the presenter wrote something different from what was intended often because of a lack of understanding of concepts, and then refused to acknowledge the error. The defense often includes semantics like 'ambiguous' designed to put the burden on someone else.
perhaps you can present some notation that you feel is ambiguous, that can then be discussed.