f A is a set and B is a subset of it, given a permutation on B which gives a subset of B, does the inverse of that permutation also give a subset of B? Hmmm?
I'm almost positive it does. Wait. If you're doing a permutation which sends B to a subset of B, then it must send B to B, since you can't send more then one element to the same place. So the permutation permutes the elements of B, and separately permutes the elements of A\B. So the the inverse just sends everything back to where it came from, and so it must also permute the elements of B. Right?
Emily - please don't read this. Thanks!
VW! Sure!
And I promise not to tell Em.
As far as I know, Devon cream is clotted cream made with milk from Devon cows. (And I think the whole clotted cream concept may have originated there.)
[And the BBC seems to agree with me -- if not the cream itself, then at least the cream tea.]
As far as I know, Devon cream is clotted cream made with milk from Devon cows. (And I think the whole clotted cream concept may have originated there.)
Okay. I noodled around the site, and they note the Double Devon Cream is a little more creamy/less buttery than their Clotted Cream. Now must try them all. Must make scones, too.
I should get some of that for my Afternoon Tea. Mmmmmmm...
Oh. They have clotted cream with Drambuie. [link]
Emily. Star Market had it? Are there still Star Markets?
Er... well, it's Shaw's now. I don't know if it still has it, though. I know Cardullo's in Harvard Square does.
Hil, here's what I'm thinking. What if A is R, B is Z, and sigma is... oh. See, I'm still having some trouble with permutations versus functions. But it doesn't say A or B have to be finite -- does permutation have to be on a finite set?
I really understand things much better in lectures. Just out of the book, I'm hopeless.
ETA: Just reread the first paragraph of the chapter, where it says, "In this section, we construct some finite groups whose elements, called permutations, act on finite sets."
Duhhhhh.
Larry's always has clotted cream. That won't help you non-Seattleites, tho.
Okay, so Hil, you're saying that sigma[B] has to be B itself, not a proper subset of B? Cause, how else could it be a permutation? (Part of my problem here is that the chapter doesn't seem to have a formal definition of permutation anywhere.*) If that's so, then it's gotta be closed under inversion (er, do we say "closed under inversion"? Isn't inversion an old term for homosexuality? Not that that has anything to do with anything, I'm just grasping at any tangent which will keep me from having to address the other two problems which might as well be written in a foreign language waaaaah!) and the set of such sigmas is a subgroup of SsubA.
Note: * except for "8.3 Definition: A permutation of a set A is a function phi from A to A that is both one to one and onto." See the problem I have with reading?
