Given a set S (say, the set of real numbers), define recursively as follows:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]A_1 = S, \quad A_n = P(S)[/itex] for n > 1 (here P(S) = power set of S).

Is this valid? I am worried because the range of this function is not specified. (In fact, I don't know what the range should be... It certainly can't be the set of all sets!)

EDIT: The formula should actually read [itex]A_1 = S, \quad A_n = P(A_{n-1})[/itex], not [itex]A_n = P(S)[/itex].

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# Is this a valid recursive definition?

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