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Feb
1
awarded  Talkative
Feb
1
comment How to work with a statement: “for all $x$, if $p(x)$ then $q(x)$” (contradiction and contraposition)
Let us continue this discussion in chat.
Feb
1
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
Feb
1
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.
Feb
1
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 $\forall x:(\lnot q(x) \rightarrow \lnot p(x))$
Feb
1
awarded  Teacher
Feb
1
answered How to work with a statement: “for all $x$, if $p(x)$ then $q(x)$” (contradiction and contraposition)
Nov
23
accepted If $\sum_{n \geq 1}X_n$ converges a.s. then $\forall a > 0: \sum P(|X_n|>a) < \infty$
Nov
23
accepted Prove $||A||_2 = max_{x \neq 0, y \neq 0}\{\frac{|\langle y,Ax \rangle|}{||x||\cdot ||y||}\}$ for $A\in \mathbb{K}^{n\times m}$
Nov
23
accepted Prove a random variable has normal distribution
Nov
23
accepted Example: Sum of non-commuting matrices is not normal
Nov
23
accepted Find angle of incomplete rotation matrix
Nov
23
accepted Determine $\frac{\partial}{\partial r} \int\!\!\!\!\!\!-_{B(x,r)} \frac{r}{n} u_{xx}(y)dy$
Nov
23
revised Number of solution pairs $(i,j)$ such that $i+jk \leq l$
edited tags
Nov
23
asked Number of solution pairs $(i,j)$ such that $i+jk \leq l$
Nov
1
accepted Distribution under null-hypothesis and type 1 error
Nov
1
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!
Oct
31
asked Distribution under null-hypothesis and type 1 error
Sep
23
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!
Sep
22
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 $z$?