2 ms·
"complete" here is a matter of analysis / topology much more than it is a matter of algebra. In some sense, the algebraic numbers are indeed important in algeb
by rocqua 5y ago
"complete" here is a matter of analysis / topology much more than it is a matter of algebra.
In some sense, the algebraic numbers are indeed important in algebra as being the 'basic' field with infinite characteristic.
You get to `R` by demanding completeness (for others reading, the demand that every converging sequence has an existing limit). I would say that the idea of limits and completeness are fundamentally topological / analytical. Which is closer to geometry than to algebra.
I think the main conclusion here is that there is good reason that the field "algebraic geometry" exists.
- contravariant 5y agoGeneral topology is a pretty far cry from geometry though. What you need for the reals isn't even directly related to the topology of R, since you just need that every set with an upper bound has a least upper bound, which is a property that many types of orders can have and which doesn't necessarily have anything to do with geometry.