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::::::* If we use only secondary sources then unfortunately I think the whole "dual" formulation has to be removed. So be it; I'll do that when I remove Cybenko + add a sketchproof for Pinkus. Best, [[User:PatrickKidger|PatrickKidger]] ([[User talk:PatrickKidger|talk]]) 17:47, 1 July 2020 (UTC)
:::::::Thanks again for your reply. (i) Regarding constructivity: you are right that whether the proofs are [[Constructive proof|constructive]] is debatable (there are many versions of the theorem based on various proof techniques), and it might not even be important for an average reader. On the other hand, what I think is important is that it is an [[existence theorem]] that is, the theorem itself does not provide a construction for the object it claims to exist (irespectively whether the proofs are constructive in the sense of formal logic). So, the statements of the theorems do not provide methods / algorithms to build networks with the claimed approximation properties (though the proofs might have constructions). In my opinion, it is a crucial point. (ii) Regarding Pinkus' theorem: I agree with you that if it has a concise and instructive proof and we can present it, then we do not really need Cybenko's proof. We might even remove the classical version of the theorem (though, its advantage is that it is the one presented by several books). (iii) About "arbitrary depth" type theorems: though we prefer secondary sources (for several reasons, e.g.,
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