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I was going to comment this exact thing. Calling this an issue with an acronym for order of operations and suggesting a paradox doesn't really make sense when the real reason for the ambiguity of the expression is because of dissension on whether the term a in a(b) in this case is 2 or 6/2.

If this had been written using a vinculum instead of a solidus (or worse, the obelus) the ambiguity would be resolved:

6

-- (1 + 2) = 9

2

versus

6

--------- = 1

2(1 + 2)

Saying that there is no recognized standard also doesn't seem accurate. What about ISO 80000-1 and ISO 80000-2? ISO 80000-1:2009 section 7.1.3 which discusses printing rules for mathematical expressions indicates:

a

--- = a / (bc), NOT a/b · c

bc

ISO 80000-2:2009(E) also states that only the vinculum and solidus are acceptable as general division operators. A colon should only be used for ratios and the obelus should. not be used at all.

There's also the Physical Review Style and Notation Guide by the American Physical Society, but if I were to choose a standard, I'd go with an internationally recognized standard.

My question is, since there are in fact published international standards regarding presenting mathematical expressions (and in part their interpretation as noted above), why isn't the academic community either aware of or using those standards when teaching, particularly in getting rid of using the obelus altogether?