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holomorphic binary operators over naturals; generalized hyper operators - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: holomorphic binary operators over naturals; generalized hyper operators (/showthread.php?tid=742) Pages:
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RE: holomorphic binary operators over naturals; generalized hyper operators - tommy1729 - 08/06/2012 that proof of convergeance seems valid. ( and used 1/n^2 as i expected ) congrats ! im not sure if we have differentiability though ... if we do im betting on uniqueness. i think we will get closer to an answer of uniqueness if we find a good solution. ( differentiable or not ) regards tommy1729 ps : off topic , but im sick ![]() RE: holomorphic binary operators over naturals; generalized hyper operators - JmsNxn - 08/08/2012 Let's start by restricting ourselves to the following set: We find that these numbers can be sequenced by Our required theorem is the following: I'll rephrase this algebraically as: I'm keeping this as a foot note. It may be beneficial to consider operators as such. It seems far less gargantuan and much more as an algebraic equation. Another formula I'm thinking I'll have to make use of is: It's sort of like a quick fundamental theorem of arithmetic. I think it encodes more data then it's letting on. Although this seems a bit trivial now. But with the inverse operator function; the inverse of: Or at least a discrete point set of when I'm hoping to sort of web together the recursion at all the points that are natural; showing from the mere fact of their existence (which requires the two requirements before) rather than computing them. I think it's pretty clear that computing this function to any degree of accuracy would need a quantum computer. Lol. I'm sorry to hear that you're sick. Hope you get well. YES!!!! I have a taylor series! I have recursion written out as a requirement using typical analytic expressions! It's all down to a recursive pattern in I'm very confident this is going to be fruitful in some way. RE: holomorphic binary operators over naturals; generalized hyper operators - Gottfried - 08/09/2012 JmsNxn - that sounds as very nice news! I hope you can go on and find something valueable! Gottfried RE: holomorphic binary operators over naturals; generalized hyper operators - JmsNxn - 08/10/2012 Right now I'm writing out some assumptions we have to put away. For example: This implies that Another one is that any continuous segment of operators is commutative or associative all the operators have to be. As well; operators in a continuous segment cannot have the same identity. The functional requirement is the following: where we have: And I can obtain Thanks for the encouragement Gottfried. Like all math; it's slow progress. Little breakthroughs from time to time. RE: holomorphic binary operators over naturals; generalized hyper operators - Xorter - 08/18/2016 All it sounds so interesting. But somewhy I cannot evaluate non-trivial problems. E. g. 3[0.5]3 or something like this. Could show me more examples, please? RE: holomorphic binary operators over naturals; generalized hyper operators - JmsNxn - 08/22/2016 this is an old scrapped idea, it ended up falling apart upon close analysis. |