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between addition and multiplication
#5
What would happen if we created this:
x {0} y = x + y
x {0.5} y = x @ y
x {1} y = x * y
x {2} y = x ^ y

And then {0.25} will be the same arithmetic-geometric algorithm of {0} and {0.5}; {0.75} will be the arith-geo-algo of {1} and {0.5}, so on and so forth.

We could then solve for x {1.5} n, n E N, since:
x {1.5} 2 = x {0.5} x

Perhaps Taylor series will be derivable giving us complex arguments.
It'd also be very interesting to see what happens with logs, i.e:
log(x {1.5} 2) = ? since normal operators undergo a transformation I wonder if something happens for these.
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Messages In This Thread
between addition and multiplication - by lloyd - 03/10/2011, 09:10 PM
RE: between addition and multiplication - by JmsNxn - 03/10/2011, 11:42 PM

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