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 between addition and multiplication JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 03/15/2011, 06:11 PM (This post was last modified: 03/15/2011, 07:45 PM by JmsNxn.) This is fucking beautiful! I've been working at this for three years now and you beat me to the punch! LOL! Do you have a closed form expression for it yet? I have so many ideas involving rational operators. And one thing that MUST be true is x {1.5} 2 = x {0.5} x If that's not true then the system doesn't meet requirements. But it wouldn't be hard to improvise a system since 0 <= q <= 1, {q} is defined. Also, I wonder if we could try to implement the laws of logarithmic semi operators into this system: q:log(x) = exp^[-q](x) q:log(x {q} y) = q:log(x) + q:log(y) q:log(x {1+q} y) = q:log(x) * y And if we implement this we can feasibly solve for a new variation of tetration. Since x {0.5} y = arithmetic/geometric limiting algo = -0.5:log(0.5:log(x) + 0.5:log(y)) = sexp(slog(sexp(slog(x)-0.5) + sexp(slog(y)-0.5)) + 0.5) Holy jesus, yes! And also, I was wondering what our identities are?, if S(q) is the identity function and x {q} S(q) = x, S(1) = 1, and S(0) = 0 obvi, but what is S(q)? I found S(0.5) = 0.7019920407 for 2 {0.5} S(0.5) = 2. I used 1000 cycles so my numbers are probably more accurate. However, sadly, S(0.5) for 3 {0.5} S(0.5) = 3 is a different number and therefore {q} has no identity. This is very sad indeed. « Next Oldest | Next Newest »