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Notations and Opinions
#35
OK, I think we need to look at all the possibilities before we go too far into determining notation.

We seem to be stuck on two things that are very closely related: auxiliary hyper-operations and iterated hyper-operations, which are practically the same things, but from two different viewpoints (an example difference is that iterated hyper-3 is auxiliary hyper-4). Since the term "auxiliary" is new and "iterated" is old and venerable, it is more appropriate to call them "iterated" hyper-operations, although either term could suffice. A comparison between the notation I used and the notation that GFR used:
however, since GFR's notation requires angle-brackets around the 'y', it prevents it from being used with slash-notation, especially for some inverse hyperops. To illustrate the difficulties, I will use GFR's instead.


Fortunately, however, we do not need a notation for auxiliary hyper-logarithms, because:


So if neccessary, this can be written which means we really don't need either my notation, nor GFR's notation for auxiliary hyper-logarithms. Also, as you can see, we also don't need a notation for the auxiliary inverse, because these can be represented by negatively iterated hyper-operations. What this means is that we only need a notation for auxiliary hyper-roots.

Andrew Robbins
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Messages In This Thread
Notations and Opinions - by andydude - 01/21/2008, 02:08 AM
RE: Notations and Opinions - by Gottfried - 01/21/2008, 06:48 AM
RE: Notations and Opinions - by GFR - 01/21/2008, 10:23 PM
RE: Notations and Opinions - by andydude - 01/22/2008, 05:04 AM
RE: Notations and Opinions - by Ivars - 01/22/2008, 08:27 AM
RE: Notations and Opinions - by andydude - 01/22/2008, 07:04 PM
RE: Notations and Opinions - by Ivars - 01/22/2008, 09:56 PM
RE: Notations and Opinions - by GFR - 01/22/2008, 10:12 AM
RE: Notations and Opinions - by Ivars - 01/22/2008, 12:57 PM
RE: Notations and Opinions - by GFR - 01/22/2008, 05:47 PM
My Notation - by James Knight - 03/25/2008, 07:58 PM
Notation needed - by bo198214 - 03/26/2008, 02:26 PM
RE: Notations and Opinions - by GFR - 03/30/2008, 12:51 AM
RE: Notations and Opinions - by andydude - 03/30/2008, 05:12 AM
RE: Notations and Opinions - by GFR - 04/04/2008, 01:20 PM
RE: Notations and Opinions - by bo198214 - 04/04/2008, 01:24 PM
RE: Notations and Opinions - by GFR - 04/04/2008, 09:53 PM
RE: Notations and Opinions - by GFR - 04/05/2008, 08:26 AM
RE: Notations and Opinions - by GFR - 04/08/2008, 10:52 AM
RE: Notations and Opinions - by GFR - 04/08/2008, 03:31 PM
RE: Notations and Opinions - by bo198214 - 04/08/2008, 04:22 PM
RE: Notations and Opinions - by GFR - 04/09/2008, 05:10 PM
RE: Notations and Opinions - by andydude - 04/08/2008, 09:04 PM
RE: Notations and Opinions - by bo198214 - 04/09/2008, 11:30 AM
RE: Notations and Opinions - by GFR - 04/10/2008, 09:15 PM



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