Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 164

symbol for true statement

When writing little proofs to write a larger one, I often try to make a chain of $iff,$ to get to an obviously true statement. I feel like it would...

Asked on 12/28/2020 by Alex SJ

2 answer

Solving the system $b+c+d=4$, $ad+bc=-8$, $a+b=5$, $cd=-8$

There is a given system of equations begin{align} ab+c+d&=phantom{-}4 \ ad+bc&=-8 \ a+b&=phantom{-}5 \ cd&=-8 end{align} I have tried to simplify it by multiplying one equation by another or...

Asked on 12/28/2020 by Karagum

2 answer

Putting an $A otimes A^{mathrm{op}}$-module structure on $operatorname{Hom}(V,V')$

Observe that given an algebra $A$, we can put a $A otimes A^{mathrm{op}}$ structure on $operatorname{Hom}(V,V')$ by $$((a otimes a')f)(v)=af(a'v)$$ Indeed, we havebegin{align*}...

Asked on 12/28/2020 by A Dragon

1 answer

Why is $int x^2e^{x^2},d(x^2)$ not proper notation?

So, as the title states. My question is about mathematical notation. Whenever my lecturer in calculus one computes an integral they do some in my opinion very redundant steps. When...

Asked on 12/28/2020 by Martin van IJcken

2 answer

Inverse Limit of Complexs and Homology

Let $mathcal{A}$ be an abelian category and denote by $D(mathcal{A})$ its derived category. Let $K_nin D(mathcal{A})$ be an inverse system of complexes in $mathcal{A}$ viewed as...

Asked on 12/28/2020

0 answer

Using $frac{{{{sin }^4}x}}{2} + frac{{{{cos }^4}x}}{3} = frac{1}{5}$ finding the value of $frac{{{{sin }^8}x}}{8} + frac{{{{cos }^8}x}}{27}$

If $frac{{{{sin }^4}x}}{2} + frac{{{{cos }^4}x}}{3} = frac{1}{5}$, then (A)${tan ^2}x = frac{2}{3}$ (B)$frac{{{{sin }^8}x}}{8} + frac{{{{cos }^8}x}}{27} = frac{1}{125}$ (C)${tan ^2}x = frac{1}{3}$ (D) ...

Asked on 12/28/2020 by Samar Imam Zaidi

1 answer

Isometric mapping of two subsets in a metric space

Let (M,d) be a metric space, and M1, M2 be two subspace of M. Edit: I forgot to mension that both M1 and M2 are dense. Suppose we have ...

Asked on 12/28/2020 by user856180

1 answer

How to show $A$ is compact in $Bbb{R}$ with standard topology?

Let $A = {0} cup { frac{1}{n}| n in Bbb{N}} subseteq Bbb{R}$. I am struggling with showing whether $A$ is compact or not. I do not even know...

Asked on 12/28/2020 by Happy Turn

4 answer

Existence of a complex sequence with given property

How to show the existence of a complex sequence $(z_n)$ with $z_nne 1, forall n$ but $lim_{ntoinfty}z_n=1$ such that $lim_{nto infty}sin(frac{1}{1-z_n})=100$? Can such a sequence be...

Asked on 12/28/2020 by Praveen

1 answer

For i.i.d random variables $X$ and $Y$, is $E[X mid sigma(X+Y)] = frac{X+Y}{2}$?

Let $X$ and $Y$ be i.i.d. random variables; we want to calculate the conditional expectation with respect to the $sigma$-algebra generated by $X+Y$: $$E [X...

Asked on 12/27/2020

1 answer

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