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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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?
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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All this equation is take advantage of the fact that when you learn PEMDAS, you haven't learned about implied multiplication yet with the parentheses but no multiplication sign.
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So the first step in PEMDAS is eliminate the parentheses. That's adding 2+2, which gives 8 ÷ 2(4). It's not unreasonable that people think, oh, I need to multiply the 2 and 4 to get rid of the parentheses. When you learn PEMDAS, that's not part of what you learn.
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This is nice, but “It works by definition” is what we’ve basically been saying. You said we’re ignorant about why, so why did this become the definition and not something else?
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People settled on what proved generally useful given the most common equations. Someone has probably written a treatise on the history of PEMDAS. But that wasn’t what I was writing about.
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