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Order of Operations is not math. It is a convention, a linguistic agreement between a writer and a reader as to how to decode a written series of symbols into mathematical concepts. Ambiguity occurs when decoders disagree on the method of decoding. If I type 10-6×2 using common western numerals and mathematical symbols, people would come up with the answer of 8. However if I were evaluating 10-6×2 as transliteration of a mahgreb arabic math expression the correct answer would be 2. This is because mahgreb Arabs do order of operations from right to left. (Follow the order of their writing) if they had intended the answer to be 8, they would have written it as 2×6-10. Doing math left to right is just a made up rule devised by Eurocentric left to right readers. It is a convention, not a rule of math. Interpreting a/bc to mean either (a/b)×c or a/(b×c) do not break "rules of math" they just define two similar but distinct decoding interpretations Using one decoding method to attempt to disprove the other is simply circular reasoning. All you need to understand is that there are calculators that use one and calculators that use other. Textbooks and journals that use both and millions of people that USE alternate interpretations to decode math expressions. None answer is universally "right" or "wrong" it is "correctly decoded" or "incorrectly decoded" according to the convention you chose to use. If your purpose is to clearly communicate your intent to your reader, write your expression with sufficient parentheses so everyone, using either convention will correctly interpret your intent.

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