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.
Debate the merits of Python's method of sorting all you want, but for
the love of all that is good and holy, please do not claim that the
current way of doing things is somehow mathematically pure. The best
explanation of the current method is that it is a compromise borne out
of the best use cases encountered as the language grew in it's infancy,
and we're stuck with it currently because it would break too much to
change things right now.
E.g.:
1 < '2' => True
'1' < 2 => False
20 < 'Five' => True
None < 0 => True
[1,2] < (1,2) => True
(1,2) < [100,200] => False
(None,) < None => False
{1:None,2:None} < [1,2] => True
[None, 1, 'five', open('README'), (1,2,3)].sort() => works just fine
[None, 1, 'five', open('README'), (1,2,3), 1j].sort() => crashes and burns
None of these make sense mathematically, nor were they motivated
primarily by mathematical arguments. Why is [1,2] < (1,2)? Because
'list' < 'tuple' - No more, no less.
One could argue that you could think of complex numbers as tuples of
values - but then why does
[(1,2),(4,1),(4,-3),(7.2,-1.2)].sort() work and
[(1+2j),(4+1j),(4-3j),(7.2-1.2j)].sort() fail?
"Practicality beats purity." Python has it's current ordering/sorting
scheme not because it is theoretically pure, but because it seemed like
the best option at the time. Please don't pretend it's perfect - it's
even been admitted that things are going to change in the future,
although I haven't yet seen a conversation where it has been made clear
exactly what will change.
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