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Are there other numerical and algebraic theories?

Anonymous Thu 12 Dec 14:53:28 2019 No.11220157 View Reply Original Report

Quoted By: >>11220170 >>11220187 >>11220188

Something different from usual naturals, reals, their algebra, etc...

Anonymous

Anonymous Thu 12 Dec 2019 15:08:52 No.11220170 Report

Quoted By:

>>11220157
What do you mean by that ?

Anonymous

Anonymous Thu 12 Dec 2019 15:09:22 No.11220172 Report

Quoted By:

Sure, finite extensions of Q and their number rings, p-adic numbers, algebraic closures of Z/pZ for prime p and many many other things.

Anonymous

Anonymous Thu 12 Dec 2019 15:15:23 No.11220187 Report

Quoted By:

>>11220157
The p-adic numbers are probably the most exotic but still "numerical" numbers.
There's also weaker systems than Peano arithmetic.
There's also richer systems than the reals.

https://en.wikipedia.org/wiki/Presburger_arithmetic
https://en.wikipedia.org/wiki/Surreal_number

If you drop the "numeric", then everything in and after Noether's ideal-theory can be seen as a variant of "arithmetic and algebra", including algebraic geometry.

Anonymous

Anonymous Thu 12 Dec 2019 15:15:36 No.11220188 Report

Quoted By:

>>11220157
literally exactly what (a lot of) abstract algebra is about

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