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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'Dirichlet's function'
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Analytic form by mrflip
Correction id: 5844
Filed on: 2005-02-10 14:47:31
Status: Accepted on 2005-03-25 20:43:06
Type: Addendum
Correction text:
The Dirichlet Function is sometimes defined to take values of 1 at rationals and 0 at irrationals:
$$
f\left(x\right) =
\left\{
\begin{array}{ll}
1 & \textrm{if } x \textrm{ is a rational number,} \\
0 & \textrm{if } x \textrm{ is an irrational number.}
\end{array}
\right.
$$
This form is everywhere discontinuous. It has an analytic expression:
$$
f(x) = \lim_{m \to \infty} \lim_{n \to \infty} cos^{2 n} (m! \pi x)
$$ |
No comment from object owner mathcam.
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