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.
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.
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...
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
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.
