I found a few typos. In the 2nd paragraph under the section “strong feelings”, you use “than” when it should be “then”. More importantly, when talking about distributive properties, you say x(x+z)=xy+xz. I believe you meant x(y+z)=xy+xz.
Otherwise, I enjoyed that read. I’m embarrassed to say that I did think pemdas meant multiplication came before division, however I’m proud to say that I’ve unconsciously known that it’s important to avoid the ambiguity by putting parentheses everywhere for example when I make formulas in spreadsheets. Which by the way, spreadsheets generally allow multiplication by juxtaposition.
It’s actually fine to do multiplication before division, you just have to be sure about which numbers are intended to be included in the divisor of your fraction!
Thank you so much for taking the time and reading the post. I just fixed the typos, many thanks for pointing them out.
There is nothing really to be embarrassed about and if you look at the comment sections of such viral math posts you can see that you are certainly not the only one. I think that mnemonics that use “MD” and “AS” without grouping like in “PE(MD)(AS)” are really to blame here.
An alternative would be to drop the inverse and only use say multiplication and addition as I suggested with “PEMA” but with “PEMDAS” one basically sets up students for the problem that they think that multiplication comes before division.
When I used to play WoW years ago I’d always put -6 x 6 - 6 = -12 in trade chat and they would all lose their minds. Adding that incorrect solution usually got them more riled up than having no solution.
You know what, this is on us. Chat GPT is just a prediction engine that tries to say what words it thinks follow a preceding prompt, and it’s looked at millions of examples (written by us) and it’s seen hapless clients and users complain about bugs and be told: “user error, works fine” so often chatGPT just thinks it’s just the culturally accepted polite response to a bug report, in the same way as responding to “thank you” with “you’re welcome”. This is a dark mirror on our profession.
I distinguish four types. There are clever, hardworking, stupid, and lazy officers. Usually two characteristics are combined. Some are clever and hardworking; their place is the General Staff. The next ones are stupid and lazy; they make up 90 percent of every army and are suited to routine duties. Anyone who is both clever and lazy is qualified for the highest leadership duties, because he possesses the mental clarity and strength of nerve necessary for difficult decisions. One must beware of anyone who is both stupid and hardworking; he must not be entrusted with any responsibility because he will always only cause damage.
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