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A comment on Connections between Abstract Algebra and High School Algebra (2015). Parent comment

Re:Connections between Abstract Algebra and High School Alge... by dboreham on Wednesday December 06, 2017 @08:29AM (#15860897)
Reading this I thought the same thing. Then I remembered one of my high school teachers telling the class that Bertrand Russell wrote a multi-volume book with the goal to prove that 1+1 = 2. At that point I realized that you don't need to work in abstract algebra in the high school mathematics curriculum, but rather you need teachers who have a deep understanding of mathematics. Unfortunately given economic reality that's hard to achieve in the present day.
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Re:Connections between Abstract Algebra and High School Alge... by wz1000 on Wednesday December 06, 2017 @10:20AM (#15861664)
It takes just a couple of lines to "prove" that 1+1 = 2. Most of the proof is simply defining 1,2,+ and =.

https://en.wikipedia.org/wiki/Peano_axioms

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Re:Connections between Abstract Algebra and High School Alge... by mrkgnao on Wednesday December 06, 2017 @09:39AM (#15861312)
The goal of Principia Mathematica was not "to prove that 1+1=2". It was meant to be a new set (ha!) of foundations for mathematics.

https://en.wikipedia.org/wiki/Principia_Mathematica

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Re:Connections between Abstract Algebra and High School Alge... by kindfellow92 on Wednesday December 06, 2017 @09:05AM (#15861086)
You only need multi volumes to prove 1 + 1 = 2 if you start with first order logic. If you start with the rules of basic arithmetic, it takes less than a page.

There is no fundamental difference when changing your starting assumptions other than one set of assumptions might prove more things than the other. From the perspective of single proof, either is equally as good. We axiomatically know basic arithmetic to be true, just as we axiomatically know first order logic to be true.

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Re:Connections between Abstract Algebra and High School Alge... by dboreham on Wednesday December 06, 2017 @11:56AM (#15862619)
Boy, I didn't realize I needed to set the explicit "irony flag" on that post! The idea is that my math teacher was making a math joke, stimulating his students' curiosity to think about deep things like "what does it mean to add and how do you prove things that seem intuitive" and informing the class that people have written serious and long books on the foundations of mathematics. None of my kids' math teachers (so far) have made any math jokes...
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Re:Connections between Abstract Algebra and High School Alge... by posterboy on Wednesday December 06, 2017 @06:31PM (#15866143)
It's not really a joke, just an understatement. Very dry humor indeed. Could be modesty or exageration, but at its core, it's true.
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Re:Connections between Abstract Algebra and High School Alge... by galobtter on Wednesday December 06, 2017 @08:45AM (#15860971)
Well I know there are entire books written to codify basic math. I don't knowing that, or say reading and understanding Russell's book, would help teach a child that 1+1 = 2
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Re:Connections between Abstract Algebra and High School Alge... by kindfellow92 on Wednesday December 06, 2017 @09:07AM (#15861101)
You don’t need to teach a child that 1+1=2, they already know it’s true. You just need to teach them what the symbols mean. Every child knows that you can put two rocks together.
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