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 Nov15 answered Eigenvalues of operator $p(T)$ in terms of the eigenvalues of $T$, where $p$ is a polynomial Nov13 revised $A\in M_2(\mathbb C)$ and $A$ is nilpotent then $A^2=0$.How to prove this? added 39 characters in body Nov12 comment If $f(x)\ge g(x)$, is $f'(x)\ge g'(x)$? Fortunately it holds that if $f\geq g$ then $\int f\geq \int g$ with some conditions on $f$ and $g$ and several flavors of $\int$. Nov12 revised Suppose $\{f_k\}$ is a sequence of $M$-measurable functions on $X$. Let $p_1$ and $p_2\in [1,\infty)$, and suppose $f_k\in L^{p_1}\cap L^{p_2}$. added 1 character in body Nov12 answered Is there a simpler proof that $f(x,y,z) = 4x + 11y + 18z$ is surjective? Nov12 revised Is there a simpler proof that $f(x,y,z) = 4x + 11y + 18z$ is surjective? Formatting Nov12 comment Prove $\sum_{n=1}^{\infty} n \mu(A_n) = \sum_{n=1}^{\infty}\mu(B_n) = \sum_{n=1}^{\infty} \mu(E_n)$ Yes, the triple equality doesn't holds in general. I misread the thing, wanted that can to be some other can't. Thank you for the clarification. Nov12 comment Prove $\sum_{n=1}^{\infty} n \mu(A_n) = \sum_{n=1}^{\infty}\mu(B_n) = \sum_{n=1}^{\infty} \mu(E_n)$ @DanielFischer I think you mean: "but it can't be that..." at the end of the integrals solution. Nov12 awarded Popular Question Nov11 comment what is the cardinality of a Null set? What kind of null set? Nov10 revised Composition of measureable function with continuou function in $L^2[0,1]$ Formatting. Nov7 comment Is there a rationality-preserving order isomorphism between $\mathbb{Q}$ and two disjoint open intervals? If there's an order preserving map between negative rationals (positive rationals) and rationals, one idea is to: send negative rationals to rationals to first interval, and positive rationals to rationals to second interval. Nov5 revised Give a counterexample to show that $(AB)^{-1} \neq A^{-1}B^{-1}$ edited title Nov4 comment Can basis vectors have fractions? @tokola If the vectors in the basis you found are just scalar multiples of the vectors in the solution from the book you should end up with the same diagonal matrix that they have. So maybe you made a mistake when calculating $P^{-1}AP$ or when calculating the power you mention. By the way, funny nickname. Nov4 revised Prove that g(y)>0 for all y in the real numbers This has nothing to do with proof theory. Nov4 comment Triangle inequality Related Nov4 revised Let $V$ be a finite dimensional real vector space and let $A:V\to V$ be a linear map such that $A^2=A$ added 143 characters in body Nov3 answered Let $V$ be a finite dimensional real vector space and let $A:V\to V$ be a linear map such that $A^2=A$ Nov1 comment On Fatou's Lemma Limit may not always exist. Oct31 awarded Popular Question