What is recursion? I've looked at the Wikipedia's explanation (recursion and then recursion in language) but that explanation is not really clear.
Recursion is a property of language.
From a Linguistics viewpoint, recursion can also be called nesting. As I've stated in this answer to what defines a language (third-last bullet point), recursion "is a phenomenon where a linguistic rule can be applied to the result of the application of the same rule."
Let's see an example of this. Consider the sentence:
An application of recursion would give:
And so on. This can go on endlessly, even if in real situations recursion will stop at a certain point, since the idea being expressed would get too confused. Recursion can also be applied to a noun and its adjectives:
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