1
$\begingroup$

The Dirichlet function is defined as:

  • if $x$ is rational, $f(x)=0$,
  • if $x$ is irrational, $f(x)=1$.

What is its support?

I think the answer is the set of irrational numbers.

$\endgroup$
3
  • $\begingroup$ Yes.${}{}{}{}{}$ $\endgroup$
    – Mario Carneiro
    Nov 20, 2014 at 4:03
  • 1
    $\begingroup$ There are multiple notions of Support of a function, and the answer depends on which one you use. You should include your definition of support in the question. $\endgroup$
    – user147263
    Nov 20, 2014 at 4:05
  • $\begingroup$ the support of a function is clusre of the set of all points where the function is non-zero $\endgroup$
    – DongTian NaXi
    Nov 20, 2014 at 4:06

1 Answer 1

Reset to default
0
$\begingroup$

Use your definition, $\{x|f\neq 0\}=\mathbb{R}\setminus\mathbb{Q}$ , whose closure is $\mathbb{R}$. So the support is $\mathbb{R}$.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .