4 ms·
> E.g., we can study the natural numbers and the integers, rationals, algebraics, and reals, but why the reals? Well, they are the only complete, Archimedean or
by BrainInAJar 12y ago
> E.g., we can study the natural numbers and the integers, rationals, algebraics, and reals, but why the reals? Well, they are the only complete, Archimedean ordered field.
Well, and the complex numbers, they're the only algebraically closed field.
- omaranto 12y ago> Well, and the complex numbers, they're the only algebraically closed field. That is very, very far from being true! There are algebraically closed fields of every characteristic and of arbitrarily large cardinality. What did you mean?
- deleted 12y ago[deleted]
- BrainInAJar 12y agosorry, "the only" was way wrong. They are, conveniently, an algebraically closed field.
- JadeNB 12y ago> > Well, and the complex numbers, they're the only algebraically closed field. > That is very, very far from being true! There are algebraically closed fields of every characteristic and of arbitrarily large cardinality. What did you mean? Although BrainInAJar seems simply to have misspoken (https://news.ycombinator.com/item?id=9254999 https://news.ycombinator.com/item?id=9254999), you have just explained one of the things that the remark could have meant: namely, that ℂ is the unique characteristic-0, algebraically closed field with the cardinality of the continuum.