[r6rs-discuss] Complex <?

[Jon Wilson]

Carl Eastlund wrote:
> Ken, I think you're missing John's point, and some crucial
> mathematical terminology.  "Real numbers" are a specific, proper
> subset of the complex numbers - specifically, those without an
> imaginary component.  In this context, the terms "real", "imaginary",
> and "complex" have nothing to do with their usual, non-technical
> meaning.  Saying that 2+3i isn't a real number doesn't mean that it
> isn't a number.

Yes, and rather crucially, the complex field is not in general an 
ordered set.  Certainly one may define an ordering upon it, but there is 
not a "standard" ordering like < for the reals.  To quote wikipedia (if 
that may be permitted), "Unlike the reals, the set of complex numbers 
cannot be totally ordered in any way that is compatible with its 
arithmetic operations: C [,the complex numbers,] cannot be turned into 
an ordered field."  Some actual attention to the mathematics is very 
much warranted here.  But, this thread really doesn't belong on 
r6rs-discuss...
Regards,
Jon