On 12/20/2009 2:33:07 PM, stuartafbruff wrote:
>Thanks, but it's not complete - it might well be desirable to sort by im then re, or by arg then modulus.
OK, but it's complete in the sense that you refer how other programs order complexes (including derive!).
>They can be sorted, IIRC re-then-im and mod-then-arg are both total orderings, but complex numbers aren't generally regarded as orderable because simple operations, such as addition and multiplication, do not preserve the order as they would when applied to reals.
You're right, complexes by itself can be sorted, but what have not order relation is the corp. In this page can find the demonstration:
http://fr.wikipedia.org/wiki/Corps_ordonn�Corp (field) is the structure that have complexes, and this is what I refer as unsorted. The total order without the structure, for this is for what I have not idea about theoretical background: can be sorted, so: for what?
The classification of order relations is
This from the spanish wiki page
http://es.wikipedia.org/wiki/Orden_total , the schema isn't in english.
Regards. Alvaro.