On Wednesday, 20 August 2025 at 17:35:20 UTC-7 tcsc...@gmail.com wrote:

Let me also point out that this is for *enumerated* sets, which means there 
is a special total order on the objects. So I might not call it arbitrary. 
However, that is somewhat of a digression.


And that order is indeed relevant! This category indeed does what it 
advertises:

sage: E=EnumeratedSets()
sage: V=E([1,2,3])
sage: W=E([1,3,2])
sage: V == W
False

so the ordering on the elements is a very fundamental property.

Also, these objects are UniqueRepresentation, so they are incredibly 
expensive to create. One should only use them when one really needs 
parent-like properties from them. You do get lightning-fast comparison 
between them once they are created, though.
 

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