Comparison of functions

[Steven D'Aprano]

On Sat, 30 Jul 2005 13:22:47 +0000, Adriano Varoli Piazza wrote:

> As far as I recall from Math Analysis, which I studied two months ago,
> you can't sort complex numbers. It makes no sense. The reason being
> (reading from my book), it's not possible to define an order that
> preserves the properties of arithmetical operations on complex numbers.
> So you can't order them, and you can't compare them.

You are confusing mathematical ordering with sorting a list. Here, I will
sort some mixed complex and real numbers for you. If you look at them
closely, you will even be able to work out the algorithm I used to sort
them.

1
1+0j
1+7j
2
2+3j
3+3j
3-3j
3+4j
4
4+2j


It was easy. I never once asked myself whether some complex number was
greater or less than another, I just asked "which one comes first in a
lexicographic sort?"

The two questions are NOT the same, and it is an ugliness in an otherwise
beautiful language that Python treats them as the same.

Mathematically, 1 == 1.0 == 1+0j but in the dictionary "1" should sort
before "1.0" which sorts before "1.0+0.0j". 



-- 
Steven.