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 Jun 11 asked How to denote domain and range Mar 18 accepted Enumerating cases for conditional probability Mar 1 accepted Understanding group presentation as a quotient Mar 1 comment Understanding group presentation as a quotient Wow, nice answer, thanks for putting in the time! I'm going to have to put in some time studying it some more to understand it, but I think I was able to follow each step, just haven't quite pulled it all together into a conclusion yet. Also, I think there's a typo in the last paragraph: you have $fef$ listed twice in $\hat{G}$. Feb 28 asked Understanding group presentation as a quotient Feb 26 accepted Show that group action is homomorphism to Symmetric group Feb 26 comment Show that group action is homomorphism to Symmetric group Oh, ok. So my original formulation for the condition of homomorphism was off. I think it makes sense now, thanks! Feb 26 comment Show that group action is homomorphism to Symmetric group Actually, I take that back, $A_g(x)$ is not a permutation of $X$, it's an element of $X$. So how can you compose a permutation/function, $A_g$ with an element of a set, $A_f(x)$? Feb 26 comment Show that group action is homomorphism to Symmetric group @SpamIAm: Thanks, but I think you over estimate me. I have the axioms written out as $A(e,x) = x$ for all $x$ (where $e$ is the identity of $G$) and $A(g, A(f,x)) = A(g+f, x)$, but it's still not clear to me why this defined a homomorphism. Feb 26 comment Show that group action is homomorphism to Symmetric group (Thanks for updating from $h$ to $A$). So the steps to change right side, $A(g+f,x)$ into $A_g * A_f(x)$ are clear, but is that necessarily equal to $A_g(x) * A_f(x)$. I know $A_g(x)$ and $A_g$ are both permutations of X, but are they they same? Feb 26 comment Show that group action is homomorphism to Symmetric group @ThomasAndrews: Thanks, I've updated the question to use $A$ in place of $h$: I'm not sure why I started using $h$, must be misread something somewhere. So if $A$ is the group action, we have $A : G \times X \to X$, to it $A$ takes a two-tuple $(g,x)$ with $g \in G$ and $x \in X$. Feb 26 revised Show that group action is homomorphism to Symmetric group edited body Feb 26 asked Show that group action is homomorphism to Symmetric group Feb 24 accepted Notation for nested sigmas (summations) Feb 21 comment Notation for nested sigmas (summations) Oh, that's right, I forgot you can iterate over a set of tuples. But it doesn't really resolve the question of how to neatly define the set from which they draw, which is kind of the big problem in the originally posted example. Feb 21 asked Notation for nested sigmas (summations) Feb 19 comment Enumerating cases for conditional probability Thanks. That's nearly what I came up with as described in the question, but it is not any more clear to me why you don't need $\binom{8}{4}$ included somewhere as this is the total number of ways in which you can choose which four bits are set and which four are cleared. Feb 18 asked Enumerating cases for conditional probability Sep 11 comment Name for the sense of how many items are present Perfect, thanks! Sep 11 accepted Name for the sense of how many items are present