Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 147

Let$A$ be an open, dense set in $mathbb R^n$. Prove that $A + A = mathbb R^n$

I have no idea how to go about this one. What I'm trying to prove is that given some $x$ in $mathbb R^n$ there has to be some...

Asked on 01/18/2021 by Francisco José Letterio

1 answer

(proposed) elegant solution to IMO 2003 P1

The problem: $S$ is the set ${1,2,...,10^6}$. Show that for any $101$ element subset $A$ of $S$ we can find $100$ distinct elements ...

Asked on 01/18/2021 by MNIShaurya

0 answer

Reverse order of polynomial coefficients of type $left(r-xright)^n$

I have a simple question. I have a polynomial defined by$$left(r-xright)^n = a_0 + a_1 x + ... + a_n x^n$$ Is there a simple expression...

Asked on 01/18/2021 by thinkingeye

1 answer

Should one include already cemented proofs of related principles in one's paper?

In a paper I'm writing (purely recreationally, nothing fancy), I state that "an odd number minus an odd number = an even number". I also state that "an even number...

Asked on 01/18/2021 by A. Kvåle

0 answer

Find the smallest $k$ such that $kx bmod n in [a,b]$

Problem: For given $x, a, b$ all reduced mod $n$, find the smallest non-zero $k$ (if any) such that $kx bmod n in [a, b]$. The...

Asked on 01/18/2021 by JP Sugarbroad

0 answer

The Cauchy-Crofton formula on a plane

For the complete tutorial for the formula you can check Do Carmo's Differential Geometry of Curves & Surfaces page through 42-46 at section 1.7. The formula $$iint n(p,theta)dpdtheta=2 Len(alpha)$$...

Asked on 01/18/2021 by Jale'de jale uff ne jale

1 answer

Solving a limit for capacity of a transmission system

I'm studying dynamical systems and I've found myself trying to solve this limit: $$ lim_{k to +infty} frac{log_{2}(frac{1}{sqrt{5}}(frac{1+sqrt{5}}{2})^k - frac{1}{sqrt{5}}(frac{1-sqrt{5}}{2})^k)}{k}$$ Till now, I changed the base of the logarithm...

Asked on 01/18/2021 by jeongbyulji

3 answer

Galois group Abstract algebra

$omega$ is the primitive $4^{th}$ root of unity, then find $Galleft(mathbb{Qleft(sqrt{2},omegaright)/mathbb{Q}}right).$ First i calculate order of $Galleft(mathbb{Qleft(sqrt{2},omegaright)/mathbb{Q}}right)$ which is $4$ by use of minimal polynomial....

Asked on 01/18/2021 by user462999

1 answer

Does there always exists coefficients $c,dinmathbb{R}$ s.t. $ax^3+bx^2+cx+d$ has three different real roots?

Well, my question is exactly the one which is written in the title. Consider $a,binmathbb{R}$ two given real numbers. Now, let $c,dinmathbb{R}$ be two parameters that we can...

Asked on 01/17/2021 by W2S

2 answer

If there is a "worldly ordinal," then must there be a worldly cardinal?

A cardinal $kappa$ is said to be worldly if $V_kappa$ is a model of ZFC. Let us (potentially) generalize this by saying an ordinal $alpha$ is...

Asked on 01/17/2021 by Jesse Elliott

2 answer

Ask a Question

Get help from others!

Mathematics : Recent Questions and Answers (Page 147)

Ask a Question