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 Feb 1 answered How do we conclude that $f(x)=0, \forall x\in \mathbb{R}$ ? Dec 18 answered How to show that $Sp\{u+v-3w,2v-w,t+w,v+w\} = Sp\{u,v,w,t\}$ Dec 16 awarded Yearling Nov 18 awarded Popular Question Nov 18 comment When data mining, how to solve the problem that the positive instances are much less than negative instances in dataset? You can find a lot of information Googling about skewed classes and logistical regression Nov 18 comment When data mining, how to solve the problem that the positive instances are much less than negative instances in dataset? stats.stackexchange.com/questions/6067/… Nov 9 accepted Proving that the maximal abelian extension contains all abelian extensions Nov 9 answered Prove the infinite union is not regular Nov 7 comment An exercise related to Krull topology - showing that two bases define the same topology @random123 - Could please you add some details ? Nov 7 asked An exercise related to Krull topology - showing that two bases define the same topology Nov 6 accepted What is a good theoretical, yet somewhat practical, book about error correction codes? Nov 6 accepted Subgroups of Index $2$ of $(\mathbb{Z}_{2})^{\aleph_{0}}$ Nov 6 comment Subgroups of Index $2$ of $(\mathbb{Z}_{2})^{\aleph_{0}}$ @AsafKaragila - I mean the one group, up to isomorphism, of order $2$. I don't know about the dyadic integers (yet ?) Nov 6 revised Subgroups of Index $2$ of $(\mathbb{Z}_{2})^{\aleph_{0}}$ added 104 characters in body Nov 6 asked Subgroups of Index $2$ of $(\mathbb{Z}_{2})^{\aleph_{0}}$ Nov 6 answered Prove that the Language $L= \{ 0^n1^m \;|\; n,m \ge 0 \}$ is regular Nov 3 awarded Enlightened Nov 3 awarded Nice Answer Nov 2 comment Checking irreducibility of a polynomial in $\mathbb{K}[x,y]$ and PAC fields Thank you for posting an answer, I think there is a counter example for your claim: Take $K=\mathbb{R}$ and $\phi=-x^{2}$ which is separable as every irreducible factor is separable. $n=2$ and the $n$-th roots of unity are $\pm1\in\mathbb{R}$. $F(x,y)=y^{2}-\phi(x)=y^{2}+x^{2}=(y+ix)(y-ix)$ is a factorization over $\mathbb{C}$ so that $F(x,y)$ is not irreducible as claimed. Did I miss something ? Nov 2 asked Proving that $Gal(K^{\text{sep}}/K)=Aut_{K}(\tilde{K})$