So what exactly is a complex number?

[Roy Smith]

In article <mailman.8.1188882659.2658.python-list at python.org>,
 Steve Holden <steve at holdenweb.com> wrote:

> Roy Smith wrote:
> > Boris Borcic <bborcic at gmail.com> wrote:
> >> Complex numbers are like a subclass of real numbers 
> > 
> > I wouldn't use the term "subclass".  It certainly doesn't apply in the same 
> > sense it applies in OOPLs.  For example, you can't say, "All complex 
> > numbers are real numbers".  In fact, just the opposite.
> > 
> > But, it's equally wrong to say, "real numbers are a subclass of complex 
> > numbers", at least not if you believe in LSP 
> > (http://en.wikipedia.org/wiki/Liskov_substitution_principle).  For example, 
> > it is true that you can take the square root of all complex numbers.  It is 
> > not, however, true that you can take square root of all real numbers.
> > 
> That's not true. I suspect what you are attempting to say is that the 
> complex numbers are closed with respect to the square root operation, 
> but the reals aren't.

Yes, that's what I was trying to say.

> I don't think "subclass" has a generally defined meaning in mathematics 

That may be true, but this is a programming newsgroup, so I was using a 
programming sort of definition.