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 Oct 1 comment Isomorphism of stabilizer over $S_n$ to $S_{n-1}$ Ok, great.${}{}{}{}$ Oct 1 comment Isomorphism of stabilizer over $S_n$ to $S_{n-1}$ There is no such thing as the stabilizer of the permutation group. Oct 1 answered Prove there are no rational numbers a, b, such that $\sqrt 3 = a + b \sqrt 2$ Oct 1 comment Permutations as a product of transpositions Good, how can we write it in a different way? The problem also asks you to show a permutation with two factorizations. Oct 1 answered $S_n$ acting on set of natural numbers Oct 1 answered How to show that if $k | n$, then $D_{2k} \leq D_{2n}$? Sep 30 answered Proving that monotonously rising functions on $[0,1]$ have at most countable points of discontinuity. Sep 30 comment If $A⊂B$, can I assume that there exists an injective function $A\to B$? Yes, you can.${}{}$ Sep 30 awarded Nice Answer Sep 30 comment How to prove $\binom{n+1}{m+1}=\binom{0}{m}+\binom{1}{m}+\dots+\binom{n}{m}$ combinatorially On the other hand I've gained like 200 rep for this question over the years. Sep 30 comment How to prove $\binom{n+1}{m+1}=\binom{0}{m}+\binom{1}{m}+\dots+\binom{n}{m}$ combinatorially If only had a penny for each time this question has been asked. Sep 30 answered What are some things we can prove they must exist, but have no idea what they are? Sep 27 answered Order of zero in $\mathbb{Z}_m$ Sep 27 comment Prove these two elements are not associated in $\mathbb Q[x,y,z]/(x-xyz)$ It is not a duplicate, the questions are clearly very different. Just because an answer to my question lies inside that question does not make it a duplicate. In other words, the duplicity between two questions should not be dependent on the answers they receive. Sep 27 comment Number of edges in a graph with n vertices and k connected components Doe this clear things up? Do you need help passing from the first sentence in red to the second sentence in red? Sep 27 comment Number of edges in a graph with n vertices and k connected components Also notice that "Otherpart" is not negative since all of its summands are positive as $n_i\geq 1$ for all $i$. Sep 27 comment Number of edges in a graph with n vertices and k connected components So $(n_1^2-2n_1+1)+(n_2^2-2n_2+1)+\dots (n_k^2-2n_+1)+other part=(n_1^2-2n_1)+(n_2^2-2n_2)+\dots + (n_k^2-2n_k)+k+otherpart=n^2+k^2-2nk$ as desired. Sep 27 comment Number of edges in a graph with n vertices and k connected components Oh ok. Well, he has the equality $(n_1-1)+(n_2-1)+(n_3-1)+\dots (n_k-1)=n-k$. So if he squares both sides he has: $((n_1-1)+(n_2-1)+(n_3-1)+\dots (n_k-1))^2=n^2+k^2-2nk$. But how do you square a sum? you have to use the distributive law right? You have to take the multiplication of every pair of elements and add them. What the author is doing is separating the sum in two parts, the squares of each element $n_i^2$ plus the products of $n_in_j$ with $i\neq j$. So he gets $((n_1-1)^2+(n_1-1)^2+\dots +(n_k-1)^2)+Other part =n^2+k^2-2nk$. Sep 27 comment Number of edges in a graph with n vertices and k connected components what part are you having trouble with? Sep 27 revised Prove these two elements are not associated in $\mathbb Q[x,y,z]/(x-xyz)$ edited body