Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 50

What are some ("small") Riesel numbers without a covering set?

In the thread Does every Sierpinski number have a finite congruence covering? some examples of proven Sierpiński numbers that seem to have no full ...

Asked on 12/06/2021 by Jeppe Stig Nielsen

1 answer

What properties a matrix need to satisfy to form a real vector space

I know the definition of vector space (i.e. it should be closed under addition and multiplication). I read in a book ('Linear Algebra done right' by Sheldon Axler) that the...

Asked on 12/06/2021

1 answer

Compactness of a Subspace of $mathbb{R}$

I am trying to determine if the following set is compact: $$A=bigg{frac{1}{n}: nin mathbb{N}, n>0bigg}subsetmathbb{R}$$ When I consider the subspace topology induced by the standard topology of $mathbb{R}$...

Asked on 12/06/2021

1 answer

Prove that $frac{d^n}{dx^n}(1-e^x)^nBigrvert_{x=0}=(-1)^nn!$

I'm not sure where to start with this. I have tried induction but I'm stuck on the inductive step. Could anyone let me know how to do this or give...

Asked on 12/06/2021 by Cand

2 answer

Finding $E in mathcal A otimes mathcal B$ such that $E neq E^y times E_x,$ for some $x in X, y in Y.$

Let $(X, mathcal A, mu)$ and $(Y, mathcal B, nu)$ be two measure spaces. What has been stated in my book is that $mathcal A times mathcal...

Asked on 12/06/2021

2 answer

Yes/ No Is $X$ is homeomorphics to $Y$?

$X={(x,y) in mathbb{R^2}: x^2+y^2=1 }$ and $Y={(x,y) in mathbb{R^2}: x^2+y^2=1 } cup {(x,y) in mathbb{R^2}: (x-2)^2+y^2=1 } $ be the subspaces of $mathbb{R}^2$ Now my...

Asked on 12/06/2021

1 answer

Is $sum_nleft(a_n^{frac{1}{n}}-1right)$ convergent?

Let ${a_n}$ is a sequence of positive real numbers and $limlimits_{nrightarrow infty}a_n^{frac{1}{n}}=1$ , then is there any condition on ${a_n}$ so that the $sum_nleft(a_n^{frac{1}{n}}-1right)$ is convergent...

Asked on 12/06/2021

1 answer

Maximum of function abs

Let function $f(x)=|2x^3-15x+m-5|+9x$ for $xinleft[0,3right]$ and $min R$. Given that $max f(x) =60$ with $xinleft[0,3right]$, find $m$. I know how to solve this kind...

Asked on 12/06/2021 by Hai Smit

1 answer

Proving that $mathbb{Z}[i]/langle 2+3irangle $ is a finite field

Prove that $mathbb{Z}[i]/langle 2+3irangle $ is a finite field.Hi. I can't try a few steps in the next solution $$mathbb{Z}[i]/langle 2+3irangle simeq mathbb{Z}[x]/langle 1+x^2,2+3xrangle$$ and $9(1+x^2)+(2-3x)(2+3x)=13$...

Asked on 12/06/2021

2 answer

Simple proof there is no continuous bijection from $mathbb{R}^n$ onto $[0,1]^m$

This is inspired by this question. Using invariance of domain or some such theorem, it is easy to prove there is no continuous bijection $f:mathbb{R}^nto [0,1]^m$ for any...

Asked on 12/06/2021 by Cronus

1 answer

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