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A comment on Math is still catching up to the genius of Ramanujan. Parent comment

Re:Math is still catching up to the genius of Ramanujan by dagw on Tuesday October 22, 2024 @04:52AM (#41912414)
The first math course as math major in university involved proving that a+b=b+a and that a+(b+c)=(a+b)+c. It's quite fun to go from 'advanced' calculus during the final classes of high school, to "OK, let's consider the expression 1+1=2. What does it actually mean and why is it true?"
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Re:Math is still catching up to the genius of Ramanujan by thaumasiotes on Tuesday October 22, 2024 @07:25AM (#41913207)
> The first math course as math major in university involved proving that a+b=b+a and that a+(b+c)=(a+b)+c.

Really? What were the axioms?

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Re:Math is still catching up to the genius of Ramanujan by dagw on Tuesday October 22, 2024 @07:32AM (#41913250)
Basically the Peano axioms
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Re:Math is still catching up to the genius of Ramanujan by thaumasiotes on Tuesday October 22, 2024 @07:43AM (#41913312)
How did that proof work for rational numbers?
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Re:Math is still catching up to the genius of Ramanujan by dagw on Tuesday October 22, 2024 @08:02AM (#41913415)
It's been 20+ years, and I don't remember the exact steps the course went thought. But basically we started with defining N using the Peano axioms (although I don't recall the name 'Peano' being mentioned) and proving some basic rules of addition and equality. Then we defined subtraction, multiplication and inverse elements, and constructed Z and Q. From there you get to algebraic groups, and from there you can hand wave a lot of details.

As I said it was literally one of the first math courses we did, so it wasn't super rigorous with all the technical and logical details.

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