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@Andydude References about the formalization of the Hyperoperations
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First of all, I believe I wrote most of the Hyperoperations article on Wikipedia. There was an existing article called "Hyper operator", but there were many people on the Talk sub-page that led me to believe that the page needed a lot of work, so I tried to do my best with the rewrite. I included every reference that I could find on the topic, and compiled what I think is a comprehensive list of references that doesn't focus on Tetration, but all hyperoperations in general.

Almost every article I've read about hyperoperations refers to them as a sequence of binary operations. This is the "specific sense" that the first part of the article is about. I don't remember ever reading about indexed families or the like, but it's the only definition that is broad and yet concise enough to describe the current usage of the word among those who use it in this area of research. Many people also use the word in the "general sense", and I wanted to be clear about what this more general idea was. If you can be even more clear about it, then be my guest. But I am concerned about Wikipedia's policies about original research. I do not believe that the definition of the "general sense" is original research because it is a natural translation of other people's terminology from 50 years ago into today's terminology. So don't think of it as: "Andrew wrote the first definition", think of it as: "this is the definition that everyone has been talking about with different words".
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RE: @Andydude References about the formalization of the Hyperoperations - by andydude - 07/17/2014, 05:29 PM

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