Owen Biesel
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 Sep19 awarded Yearling Jan13 comment If $A \hookleftarrow B \to R$ each contain $R$, is $R\to A\otimes_B R$ injective? I had also found the similar example $B=R[x]$, $A = B[x^{-1}]$, and $B\to R$ sending $x\mapsto 0$. Thanks for tying off this loose question! Jan13 accepted If $A \hookleftarrow B \to R$ each contain $R$, is $R\to A\otimes_B R$ injective? Dec12 answered Limit of series $4\left( \frac {1}{8}+\frac {1}{12}\right) +6\left( \frac {1}{24}+\frac {1}{36}\right) +\ldots$ Dec12 comment Prove that if $7$ divides $6^n + 1$ then $n$ is odd Just to note: You have written the inverse, not the contrapositive. The contrapositive would be "If $n$ is not odd, then $7$ does not divide $6^n + 1$." Sep20 accepted Are automorphisms of extensions trivial? Sep20 comment Are automorphisms of extensions trivial? In fact, $0\to \mathbb{Z}/(2) \to \mathbb{Z}/(4) \to \mathbb{Z}/(2) \to 0$ with the automorphism $f:a\mapsto -a$ also works. Sep20 comment Are automorphisms of extensions trivial? Specifically, $0\to \mathbb{Z}/(3) \to \mathbb{Z}/(9) \to \mathbb{Z}/(3) \to 0$ with the automorphism you give. Excellent, thanks! Sep20 asked Are automorphisms of extensions trivial? Sep19 awarded Yearling May1 answered Help understanding why a block code can correct up to (d-1)/2 errors. Apr12 comment The last few digits of $0^0$ are $\ldots0000000001$ (according to WolframAlpha). "But the limit is $1$ if $f,g$ are both analytic..." What about $f(x)=0$, $g(x)=x$? I'm not sure what the missing condition is. Apr12 comment Cross product with orthonormal basis It does if you meant to write $(f_{u_1}(p),f_{u_2}(p),f_{u_3}(p))\times(g_{u_1}(p),g_{u_2}(p),g_{u_3}(p))$. Then you're taking the cross product of the same two vectors on each side of the equation. Apr12 answered Expectation value of pure state in quantum mechanics Apr12 answered Is $Ϝ$ an equivalence relation? Feb8 answered Given a diagonalizable matrix A, must $A^2$ and $A$ be row equivalent? Nov20 comment How do we represent this event? The CDF is the probability that $M$ is any value up to $x$: $P(M < x) = 1 - P(M\geq x) = 1 - (1-x)^2$. The PDF is the derivative of the CDF: $d(1-(1-x)^2)/dx = 0 - 2(1-x)^1 (-1) = 2(1-x)$. Nov19 comment How do we represent this event? Both -- the area in the plane is the probability of the corresponding event, since $X$ and $Y$ are independent and uniform. I've edited to elaborate. Nov19 revised How do we represent this event? added 358 characters in body Nov19 answered How do we represent this event?