Why `sort()` need `T` to be `Ord`?

[steffahn]

@jdahlstrom

Is there even precedence for objects that behave like IEEE floats in mathematics?

Yes, I did find "partial preorder" which matches, as mentioned somewhere above in this thread.. ah here it is:

@steffahn

For the record, f32 and f64 do actually form partial preorders. They do fulfill the additional constraint that a <= b implies a <= a and b <= b . (Called "partial reflexivity", or "reflexivity where the relation is defined" in the German Wikipedia article.) So if PartialOrd is just about giving a trait that floating point numbers can implement, then "partial preorder" rather than "transitive relation" would've been a valid choice, too.

Admitted, one cannot really necessarily call this notion

@jdahlstrom

more-or-less commonly used terminology

if it isn't even (really, AFAICT) possible to find the definition in the English Wikipedia.

But alas, "reflexive relation" isn't too out-of-the-world either, and that's apparently (according to my interpretation of the docs) what PartialOrd is all about. Of course the alternative interpretation of "if you leave out this NaN element, it's a total order, but NaN is incomparable with everything and not even equal to itself" is a totally mathematical apt description.

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@jdahlstrom

NULL in SQL has similar semantics but seems more sane in that it embraces true three-valued logic

Might be more sane; but note that (as far as my mathematical experience goes) three-valued logic is not generally the most common thing used in "mathematics". Your average mathematician would probably be happier with the "transitive relation" or even the "partial preorder".