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 Reihenalgebra andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 09/24/2007, 10:29 PM I think one of Markus Mueller's most interesting discussions is that of his arrows in and of themselves, not exactly how he defines them, though. He defines them with implicit exponentiation, whereas Knuth's arrows use implicit multiplication, a major problem between the two systems. But I think using Mueller's arrow, so much about iteration is much easier to express: $x ({\uparrow}A) y = x A (x A \cdots A (x A x))$ $x ({\downarrow}A) y = ((x A x) A \cdots A x) A x$ Using $x{\uparrow}y = x({\uparrow}\cdot)y = x^y$ (Knuth) instead of $x{\uparrow}y = x({\uparrow}\^)y = {}^{y}x$ (Mueller) we can still use the notation for both higher and lower hyper-operation hierarchies, as well as iteration itself. The iteration of a function has been written in various ways in this forum making $f^{[n]}(x) = f^{\circ n}(x) = (f {\uparrow} \circ n) \circ x$ yet another notation we could use. The only advantage of this would consistency, which we could get from using any notation if we used it a lot. Andrew Robbins « Next Oldest | Next Newest »

 Messages In This Thread Reihenalgebra - by Gottfried - 08/12/2007, 05:34 PM RE: Reihenalgebra - by bo198214 - 08/12/2007, 06:00 PM RE: Reihenalgebra - by bo198214 - 08/13/2007, 04:29 AM RE: Reihenalgebra - by jaydfox - 08/13/2007, 05:42 AM RE: Reihenalgebra - by bo198214 - 08/13/2007, 01:41 PM RE: Reihenalgebra - by andydude - 09/24/2007, 10:29 PM

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