08/10/2009, 10:03 PM
(08/10/2009, 06:15 PM)Tetratophile Wrote: so make iter[] an operator like i said. how are we gonna pronounce it anyway.As Henryk says - "iter"/"abel" are not (good) prefixes. But anyway nice words: they makes the others prefixes: (taking your proposal
Tetratophile Wrote:just make iter[] an operator on functions. then we can square it like any other operators. iter^2 means doing iter twice.
iter^-1[] is the inverse of iter[], it extracts the function you built the iter-function out of. so iter^-1[tetra-exponential]= exponential. this is more generalizable.
also, abel[f] := [iter(f)]^-1, iter[f] considered as a function.
examples:
iter-addition is multiplication, abel-addition is division
iter-iter-addition is exponentiation, abel-iter-addition is logarithm,
we can call the tetrational iter-iter-iter-addition, or iter^3-addition, and tetralogarithm abel-iter^2-addition.
iter^N-addition is (N+1)-ation, abel-iter^(N-1)-addition is N+1-logarithm.
we may be able to do away with all the hyper-n-operator s*it.
addition-abel = division
addition-iter = multiplication ...
multiplication-abel = ...
iter-abel = <...oh good grief...>
G
Gottfried Helms, Kassel