Proposal: min(None, x) and max(None, x) return x

[Pearu Peterson]

On 22 Nov 2002, Andrew Koenig wrote:

> Eric> So I told myself: wouldn't it be great if max(None, x) or
> Eric> min(None, x) always simply returned x?
> 
> My first thought was that this was an excellent idea.
> 
> Then I thought again.
> 
> Here's the problem:  The notion that max(None, x) and min(None, x)
> should both return x is one of three desirable properties that cannot
> all be true at once.  Here are the other two:
> 
>         1) Whenever x < y, min(x, y) is x and max(x, y) is y.
> 
>         2) < is an order relation over all types.
> 
> The desirability of (1) should be obvious.  (2) is more subtle, but
> it is necessary for it to be possible to sort a vector of heterogenously
> typed objects.
> 
> Now, if max(None, x) and min(None, x) both yield x, and (1) is true,
> then x > None and x < None must both be true. 

If max(None, x) and min(None,x) both yield x, then already (1) cannot be
true. For example, take x=None in (1). Then 

 min(None, y) is None and max(None, y) is y

But this contraticts the assumption that min(None, x) is x.

> But then (2) cannot be true.

(2) is never true. Hint: complex numbers.


Pearu