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Pentation's definitional ambiguity
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(10/17/2009, 09:54 PM)Base-Acid Tetration Wrote: As we all know, tetration ... has an infinite number of branches.

Yes, but what kind of infinity? I'm still not convinced that the branches of tetration are even countable. Granted, we can assign the main branch as 0, then count out which branchpoint we want, then index each branch around that branchpoint. This would give us 2 indices for each branch, but then there is the issue of branches above and below everywhere else. Are these indexable in such a manner? or do we need to add more indices to account for these?

(10/17/2009, 09:54 PM)Base-Acid Tetration Wrote: This is a highly subjective question that won't be settled by any amount of attempted rigor, so I propose a split up classification of pentations that we will study. I think we should define "proper pentation" as the function that has pen(z+1)= Tet(pen(z)), where Tet = mainly prinicipal branch of tetration. Or can't we study properties that will apply for all pentations?

Hehe, even tetration is a highly subjective function. It is very recent that tetration approaches seem to be hinting at a unified analytic continuation of all approaches. And we still aren't sure if this is really the case. In the beginning it was a lot of guesses and hunches, which led to many different tetrations, and I personally had a lot of fun studying the differences between all tetrations (and I still do). So I think it would also be a lot of fun studying all pentations too. Smile

Andrew Robbins
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Messages In This Thread
RE: Pentation's definitional ambiguity - by andydude - 10/22/2009, 07:54 AM
Number of branches of tetration - by bo198214 - 10/24/2009, 09:27 AM
RE: Number of branches of tetration - by bo198214 - 10/24/2009, 01:20 PM
RE: Number of branches of tetration - by bo198214 - 10/24/2009, 02:01 PM

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