On Mar 21, 9:05 am, Benjamin Jones <benjaminfjo...@gmail.com> wrote:
> It seems to me that the ambiguity arises from the original statement,
Systems like magma (and I assume gap as well) solve this by having a
"GSet" type. If you have S3 acting on the GSet V={1,2,3} then, one can
construct the powerset W of V as a GSet as well. In that context there
is a natural distinction between the subset {1,2,3} of V (which is a
sub-GSet) and the element {1,2,3} of W.
One can talk about the orbit of the element {1,2} in W under S3 but
obviously, {1,2} is not a sub-GSet of V.
How these things coerce between each other is another matter, but I
suspect making such distinctions internally is unavoidable.
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