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A fake Facebook event disguised as a math problem has been one of its top posts for 6 months
(www.engadget.com)
This is a most excellent place for technology news and articles.
Maybe I'm wrong but the way I explain it is until the ambiguity is removed by adding in extra information to make it more specific then all those answers are correct.
"I saw her duck"
Until the author gives me clarity then that sentence has multiple meanings. With math, it doesn't click for people that the equation is incomplete. In an English sentence, ambiguity makes more sense and the common sense approach would be to clarify what the meaning is
100% with you. "Left to right" as far as I can tell only exists to make otherwise "unsolvable" problems a kind of official solution. I personally feel like it is a bodge, and I would rather the correct solution for such a problem to be undefined.
It's so we don't have to spam brackets everywhere
9+2-1+6-4+7-3+5=
Becomes
((((((9+2)-1)+6)-4)+7)-3)+5=
That's just clutter for no good reason when we can just say if it doesn't have parentheses it's left to right. Having a default evaluation order makes sense and means we only need parentheses when we want to deviate from the norm.