That's a super fair point. I guess to me it matters more that it has all the usual field behaviors with the reals as a subset, but it is the first step "up" the

That's a super fair point. I guess to me it matters more that it has all the usual field behaviors with the reals as a subset, but it is the first step "up" the hierarchy where you lose something instead of just gaining. I'm sort of used to substituting a metric in for order, but that obviously doesn't work everywhere.