Owen Biesel
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 Oct 5 comment How many multiples of X lie in the arbitrary range [Y,Z]? That's why we use the floor $\lfloor\ \rfloor$ and ceiling $\lceil\ \rceil$ functions: if $Z/X$ (or $Y/X$) isn't an integer, we round down (or up) to the nearest. Sep 19 awarded Yearling Sep 19 awarded Yearling Jan 13 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! Jan 13 accepted If $A \hookleftarrow B \to R$ each contain $R$, is $R\to A\otimes_B R$ injective? Dec 12 answered Limit of series $4\left( \frac {1}{8}+\frac {1}{12}\right) +6\left( \frac {1}{24}+\frac {1}{36}\right) +\ldots$ Dec 12 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 $6^n + 1$." Sep 20 accepted Are automorphisms of extensions trivial? Sep 20 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. Sep 20 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! Sep 20 asked Are automorphisms of extensions trivial? Sep 19 awarded Yearling May 1 answered Help understanding why a block code can correct up to (d-1)/2 errors. Apr 12 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. Apr 12 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. Apr 12 answered Expectation value of pure state in quantum mechanics Apr 12 answered Is $Ϝ$ an equivalence relation? Feb 8 answered Given a diagonalizable matrix A, must $A^2$ and $A$ be row equivalent? Nov 20 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: $d(1-(1-x)^2)/dx = 0 - 2(1-x)^1 (-1) = 2(1-x)$. Nov 19 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.