On Wednesday, February 27, 2019 at 2:17:06 PM UTC-8, John H Palmieri wrote:
>
> Why does Sage allow inequalities in Z/nZ?
>

I'm pretty sure that it's a historical artifact from Python 2, where 
inequality relations exist between nearly all objects, because "cmp" is 
3-valued. None of the usual axioms are required or enforced. It had a nice 
consequence that "sort" would work on almost every list; possibly with 
deterministic results.

Python 3 remedied this horrible wart in Python 2, setting a nice example 
for sage to move away from having mathematically unmotivated inequalities.
With "cmp" stamped out, and the only mechanism for implementing relations 
being "richcmp", where "==" and "<" use different code paths, we can reopen 
https://trac.sagemath.org/ticket/3936 and fix this stuff (gradually). Yay!

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