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 Zeration reconsidered using plusation. MphLee Fellow Posts: 95 Threads: 7 Joined: May 2013 10/23/2015, 03:39 PM (This post was last modified: 10/23/2015, 04:56 PM by MphLee.) It is not exactly the supefunction of zeration (max-kroenecker delta definition)...but it is the superfunction of Bennett's base 2 preaddition $\odot_{-1}$ (-1th rank in base 2 commutative hos hierarchy). $A\odot_{i} B=\exp_2^{\circ i}[\log_2^{\circ i}(A) +\log_2^{\circ i}(B)]$ $A\odot_0 B=A+B$ $A\odot_{-1} B=\log_2(2^A +2^B)$ In fact you are right: define plusation (set it as rank 1 of a new sequence) $b(+)_1x=b+\log_2(x)$ $b(-)_1 x=2^{x-b}$ Let's take it's subfunction in the variable x (i.e.$F\mapsto f$ where $F(x+1)=f(F(x))$ ) $b(+)_0x=b(+)_1(1+b(-)_1 x)=\log_2(2^{x}+2^b)=b\odot_{-1}x$ But the sequence $(+)_t$ doesn't seem much interesting or natural imho... the only nice properties are that 1) it is based on the usual recursion/iteration law (ML $b*_{i+1}x+1=b*_i(b*_{i+1}x)$ ) 2) it intersects the 2-based commutative hos sequence at t=0 ($b(+)_0x=b\odot_{-1}x$) MathStackExchange account:MphLee « Next Oldest | Next Newest »

 Messages In This Thread Zeration reconsidered using plusation. - by tommy1729 - 05/29/2015, 08:07 AM RE: Zeration reconsidered using plusation. - by MphLee - 10/23/2015, 03:39 PM

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