If you thought 8 ÷ 2(2+2) = ? was stupid and pointless, so did a lot of mathematicians.https://nyti.ms/2YKDk9f
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What are the reasons and why does it make sense? I'll admit I really don't know the answers to either of those, and I mainly use it out of convention so that I can figure out what a badly written bit of code will do. Your article doesn't get into that.
The conventions of PEMDAS are fine and indeed essential for performing calculations. The equation in question is deliberately constructed to mislead people to do the "wrong" thing. There's no there there.
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That's great, but you really do have me wondering: WHY does PEMDAS make sense? You've raised the question (by pointing out our ignorance), so why did a bunch of STEM guys at some conference somewhere many, many years ago decide this was the way to go?
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It works by definition. If there were no pre-defined order of operations, you would have throw parentheses everywhere to show the intended order of operations. What PEMDAS does is simplify the notation.
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