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#math
<gzl> t sends 2 to 3 and 3 to 2 and fixes 1
<gzl> etc
<cyclicFifths> thanks gzl
<cyclicFifths> :)
<asphyxia> gzl: Nice, but it still doesnt quite explain my problem
<asphyxia> (As I see it)
<gzl> do you not see that (1 2)(2 3) = (1 2 3)?
<asphyxia> gzl I see that
<asphyxia> the transpositions all map a_1 to some different element
<gzl> do you then see that (1 2)(2 3)(3 4) is probably (1 2 3 4)?
<asphyxia> but I do not see that (1 2) (1 3) = (1 2 3)
<asphyxia> which is what my book states.
<gzl> because that's not true
<gzl> (1 2)(1 3) sends 2 to 1, not to 3
<gzl> ohh
<gzl> they're doing it the other way around
<gzl> you have to be careful of the order
<gzl> they're using st(x) = t(s(x))
<asphyxia> ehm?
<gzl> the way I wrote it, you apply them right to left (like functions). your book is going left to right.
<asphyxia> all I have is that (1 2 ... p) = (1 p) (1 p-1) (1 p-2) ... (1 3) (1 2)
<gzl> if you go right to left, as I did in my example, what your book says is equivalent to:
<gzl> (1 3)(1 2) = (3 1)(1 2) = (3 1 2) = (1 2 3)
<gzl> the issue is that if you're composing functions you need to be careful about the order in which they're being composed. f then g is not the same as g then f. you can define the multiplication either way, you just need to be consistent.
<asphyxia> if that is all there is to it, couldnt I just go do (1 p)(1 p-1) = (p 1)(1 p-1) = (p 1 p-1) = (1 p-1 p)?
<gzl> yes
<asphyxia> I dont actually think that the composition is the other way around. then it would be the first time
<asphyxia> it would be kind of odd, as permutations were composed 'normally' - I dont see why it should be the other way around with cycles.
<gzl> I don't know. be careful. if you're going right to left, (1 2)(1 3) = (2 1 3) = (1 3 2), not (1 2 3)
<gzl> I don't know what your book is saying. as far as I'm concerned now you should be able to figure it out for yourself
<gzl> this is all that's going on
<asphyxia> I think I'll translate it and tex it, if you are interested.
<gzl> I'm not, sorry.
<asphyxia> haha. I guessed so. Its not that long though, perhaps you could read it. It is a kind of proof why it is true.
<asphyxia> I'll do it anyway, hoping that someone clicks my link :)
<gzl> what you said at the beginning works fine
<gzl> are you sure your book said (1 2)(1 3) = (1 2 3)?
<gzl> I'm suspicious that it actually says that.
<gzl> er, doesn't actually say that
<gzl> that is the only inconsistent thing you've said
<asphyxia> gzl: I'll tex that part. Done in 3 minutes
<gzl> dude, isn't your question just about (1 p)(1 p-1)...(1 2)? there is no need to tex anything
<gzl> if you think (1 2)(1 3) is an example of a product like that you're just blatantly getting the order backwards
<Steve|Office> I've heard of books going in that order.
<gzl> so have I, but I think he is making the mistake in thinking that (1 2)(1 3) is an example of a product of that form
<Steve|Office> I guess I didn't read the first bit.
<gzl> anyway, let him waste time texing it if he wants, I guess
<DemisM> (1 2)(1 3) can be either of (1 3 2) or (1 2 3) right?
<gzl> no, it's only one or the other depending on which order you want to go in.
<gzl> or is that what you meant
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