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 Notations and Opinions bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 03/29/2008, 05:15 PM (This post was last modified: 03/29/2008, 05:17 PM by bo198214.) Quote:b [3] k = b ^ k = y --> b = y /[3] k = k-srt y, k = b [3] \ y = b-slog y. In other words, for rank 3 and > 3, we are in contrast with the traditional prefixed notation of the inverse operations. I dont see this contrast, we have: $y /[3] k=y^{1/k}$ and $b [3]\backslash y = \log_b y$ (And by this you can easily remember that / corresponds to the root type.) I mean the side is anyway arbitrary, you also have ${^n x}$ but you write x[4]n. GFR Wrote:The advantage of this schematical notation is that we could admit an upside-down mirror inversion of the operation symbols, in their inverse sequence, like (see the third line): ... In general, for: y = b [n] k, we might have: b = k \n| y = y /n| k, the root-type left-inverse, and k = b |n\ y = y |n/ b, the log-type left-inverse. But Gianfranco thats confusing! \ and / for the same operation depending on which side. I dont want to first think a minute what is meant by the current symbol! There is also no mnemonics attached. Neither is a both side variant really needed nor is it usual to have it. There is no opposite side variant for -, / or ^. So if you really desperately need the both-side variants then keep the same operation symbol! E.g. /n| and |n/ as root-type inversion, but I dont see usage for them. And you have to burden your memory with another rule to decide on which side is the base/exponent, i.e. on the side which is not |. However I see a bit a problem with /n|, as when you use it without spaces it can be confusing, for example |a/n|x| = | a /n| x | I placed some attention to this problem when I was deciding for /[n] because you can not misread the / as a division (because it is followed by an open bracket). This ruled out the other variant that I had in mind: /n/. However your idea to put [n]\ instead of \[n] is a better one as you can better memorize the rule b[n]k /[n] k = b and b [n]\ ( b[n] k ) = k as "The thing to be reduced is on the (reducing) operation side (i.e. the side with the / or \ attached)" PS: We can call this the BO-GFR simplified ASCII notation, however by such discussions there always comes up the image of a commitee designing conventions (by long and intense democratic discussions) which dont fit real needs of the using people. While really useful things are made without commitees! However I hope its not the case here. « Next Oldest | Next Newest »

 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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