Lesson plan
Escaping set
In mathematics, and particularly complex dynamics, the escaping set of an entire function f consists of all points that tend to infinity under the repeated application of f . That is, a complex number z_0\in\mathbb{C} belongs to the escaping set if and only if the sequence defined by z_{n+1} := f(z_n) converges to infinity as n gets large. The escaping set of f is denoted by I(f) . For example, for f(z)=e^z , the origin z=0 belongs to the escaping set, since the sequence 0,1,e,e^e,e^{e^e},\dots tends to infinity.
Article summary
In mathematics, and particularly complex dynamics, the escaping set of an entire function f consists of all points that tend to infinity under the repeated application of f . That is, a complex number z_0\in\mathbb{C} belongs to the escaping set if and only if the sequence defined by z_{n+1} := f(z_n) converges to infinity as n gets large. The escaping set of f is denoted by I(f) . For example, for f(z)=e^z , the origin z=0 belongs to the escaping set, since the sequence 0,1,e,e^e,e^{e^e},\dots tends to infinity.
Key claims
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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?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.