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 Feb1 awarded Talkative Feb1 comment How to work with a statement: “for all $x$, if $p(x)$ then $q(x)$” (contradiction and contraposition) Feb1 comment How to work with a statement: “for all $x$, if $p(x)$ then $q(x)$” (contradiction and contraposition) The tautologies (K.0)-(K.1) on this sheet might be useful to you: math.ethz.ch/~halorenz/4students/logikGT/Tautologien.pdf Feb1 comment How to work with a statement: “for all $x$, if $p(x)$ then $q(x)$” (contradiction and contraposition) No, $\forall x(p(x) \rightarrow q(x))$ is equivalent to $\forall x:(\lnot p(x) \lor q(x))$ That's right, we leave the outer quantifier be. Feb1 comment How to work with a statement: “for all $x$, if $p(x)$ then $q(x)$” (contradiction and contraposition) Because $p \rightarrow q$ is logically equivalent to $\lnot p \lor q$. Since $\lnot q \rightarrow \lnot p$ is the contraposition of $p \rightarrow q$ your statement is equivalent to $\forall x:(\lnot q(x) \rightarrow \lnot p(x))$ Feb1 awarded Teacher Feb1 answered How to work with a statement: “for all $x$, if $p(x)$ then $q(x)$” (contradiction and contraposition) Nov23 accepted If $\sum_{n \geq 1}X_n$ converges a.s. then $\forall a > 0: \sum P(|X_n|>a) < \infty$ Nov23 accepted Prove $||A||_2 = max_{x \neq 0, y \neq 0}\{\frac{|\langle y,Ax \rangle|}{||x||\cdot ||y||}\}$ for $A\in \mathbb{K}^{n\times m}$ Nov23 accepted Prove a random variable has normal distribution Nov23 accepted Example: Sum of non-commuting matrices is not normal Nov23 accepted Find angle of incomplete rotation matrix Nov23 accepted Determine $\frac{\partial}{\partial r} \int\!\!\!\!\!\!-_{B(x,r)} \frac{r}{n} u_{xx}(y)dy$ Nov23 revised Number of solution pairs $(i,j)$ such that $i+jk \leq l$ edited tags Nov23 asked Number of solution pairs $(i,j)$ such that $i+jk \leq l$ Nov1 accepted Distribution under null-hypothesis and type 1 error Nov1 comment Distribution under null-hypothesis and type 1 error Taking your comments on board I decided to see if I could prove directly that $T$ would have a normal distribution via characteristics function and I got $\frac{T}{\sqrt{n}} \sim N(\sqrt{n}\mu_0, \sigma^2)$. Could you perhaps elaborate how you got your result? Thanks for your help! Oct31 asked Distribution under null-hypothesis and type 1 error Sep23 comment Determine $\frac{\partial}{\partial r} \int\!\!\!\!\!\!-_{B(x,r)} \frac{r}{n} u_{xx}(y)dy$ Thank you, I think I've got it now! Sep22 comment Determine $\frac{\partial}{\partial r} \int\!\!\!\!\!\!-_{B(x,r)} \frac{r}{n} u_{xx}(y)dy$ Does this mean that $B(x,r)$ becomes $B(x,1)$ and then the integral over $z$?