03/16/2011, 05:47 PM
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
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
