Lesson plan
Dirichlet function
In mathematics, the Dirichlet function is the indicator function \mathbf{1}_\Q of the set of rational numbers \Q over the set of real numbers \R , i.e. \mathbf{1}_\Q(x) = 1 for a real number if is a rational number and \mathbf{1}_\Q(x) = 0 if is not a rational number (i.e. is an irrational number). \mathbf 1_\Q(x) = \begin{cases} 1 & x \in \Q \\ 0 & x \notin \Q \end{cases} It is named after the mathematician Peter Gustav Lejeune Dirichlet. It is an example of a pathological function which provides counterexamples to many situations.
Article summary
In mathematics, the Dirichlet function is the indicator function \mathbf{1}_\Q of the set of rational numbers \Q over the set of real numbers \R , i.e. \mathbf{1}_\Q(x) = 1 for a real number if is a rational number and \mathbf{1}_\Q(x) = 0 if is not a rational number (i.e. is an irrational number). \mathbf 1_\Q(x) = \begin{cases} 1 & x \in \Q \\ 0 & x \notin \Q \end{cases} It is named after the mathematician Peter Gustav Lejeune Dirichlet. It is an example of a pathological function which provides counterexamples to many situations.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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