Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $D_n$ be the open disc of radius $n$ with centre at the point $(n,0)\in\mathbb{R}^2$. Does there exist a function $f:\mathbb{R}^2\to\mathbb{R}$ of the form $f(x,y)=ax+by$ such that $$\cup_{n=1}^\infty D_n=\{(x,y)\mid f(x,y)>0\}\;?$$ If your answer is 'Yes', give the values of $a$ and $b$.

(original image)

The given set is open set, I think a function $f(x,y)=x$ or $y$ can do the job, but I am not sure, I also want to know whether inside the question any deep result is hidden from analysis.

share|cite|improve this question
up vote 6 down vote accepted

Hint: Note that $\cup_{n=1}^\infty D_n=\{(x,y)\in\mathbb{R}^2\mid x>0\}$.

enter image description here

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.