Extend the domain of maximum and minimum to include empty collection?

[klacru]

There seems some resistance and some technical difficulties to extend the domain of maximum or minimum to include empty collections.
Conforming to a proposal

@StefanKarpinski

Defining min and max to compute intersection and union has a certain appeal, but I don’t think it’s what people would really expect, and as noted would be inefficient. It seems more appropriate to introduce generic meet and join operations.

and

@jpiitula

The name join is already used for other purposes, without a corresponding meet, whereas supremum and infimum, sup and inf, lub and glb seem quite free (or if used in packages, perhaps mean more or less the same as proposed here).

I would propose to

• document the current behaviour of maximum and minimum and leave it as it is.
• implement new functions supremum and infimum, which behave equivalent for non-empty collections of totally ordered types, but cover the other cases as well.