max(), sum(), next()

[Manu Hack]

On Fri, Sep 5, 2008 at 11:45 PM, Steven D'Aprano
<steve at remove-this-cybersource.com.au> wrote:
> On Fri, 05 Sep 2008 22:20:06 -0400, Manu Hack wrote:
>
>> On Fri, Sep 5, 2008 at 1:04 PM, castironpi <castironpi at gmail.com> wrote:
> ...
>>>> >The reason sum([]) is 0 is that sum( [ x ] ) - x = 0.
>>>>
>>>> It doesn't make sense to me.  What do you set x to?
>>>
>>> For all x.
>>
>> But then how can you conclude sum([]) = 0 from there?  It's way far from
>> obvious.
>
> I think Castironpi's reasoning is to imagine taking sum([x])-x for *any*
> possible x (where subtraction and addition is defined). Naturally you
> always get 0.
>
> Now replace x by *nothing at all* and you get:
>
> sum([]) "subtract nothing at all" = 0
>
> I think that this is a reasonable way to *informally* think about the
> question, but it's not mathematically sound, because if you replace x
> with "nothing at all" you either get:
>
> sum([]) - = 0
>
> which is invalid (only one operand to the subtraction operator), or you
> get:
>
> sum([0]) - 0 = 0
>
> which doesn't involve an empty list. What castironpi seems to be doing is
> replacing "nothing at all" with, er, nothing at all in one place, and
> zero in the other. And that's what makes it unsound and only suitable as
> an informal argument.

Actually it's even more natural to state sum([x]) = x, and this way
you can never conclude that sum([]) = 0 from there.