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between addition and multiplication
#27
x {1.5} 2 = x {0.5} x

This is the general requirement that rational operators be recursive.

Consider,
x {0} y = x + y
x {1} y = x * y
x {2} y = x ^ y
x {3} y = x ^^ y

x * 2 = x + x
x {1} 2 = x {0} x

x ^ 2 = x * x
x {2} 2 = x {1} x

x ^^ 2 = x ^ x
x {3} 2 = x {2} x

etc etc...
It only be natural that this law holds for rational operators.
Generally, if {r} is any operator, than {r+1} is the superfunction of {r}.

the law stated mathematically is:

(x {r+1} (n-1)) {r} x = x {r+1} n
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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 - 03/16/2011, 05:47 PM

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