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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. 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., it helps identifying what is more important), the usage of primary sources is not forbidden (furthermore, see the last pillar of [[WP:5p]]: "Wikipedia has policies and guidelines, but they are not carved in stone"). As there are not many secondary sources about the arbitrary depth case, we could use primary sources (as I think these versions show an important development). I think that both the L1 version and your theorem is nice and I would keep both of them. What do you think? [[User:Koertefa|''<span style="color:#2F4F4F">'''K'''<span style="color:Teal">œrte</span>'''F'''</span><span style="color:Teal">a</span>'']] [[User talk:Koertefa#top|<span style="color:#2F4F4F">'''{'''<i style="color:Teal">ταλκ</i>'''}'''</span>]] 14:30, 3 July 2020 (UTC)
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