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changing terminology (was: overview paper co-author invitation)
#16
and some special prefixes for hyper-operations:

for the two functions x[N]a and a[N]x, add greek prefixes for N.

just say "N-ation" for the hyper-N-operation itself,
"N-power" for x[N]a; "N-root" for the inverse of N-power;
"N-exponential" for a[N]x, "N-logarithm" for the inverse of N-exponential

example:
tetra-power, tetra-exponential
tetra-root, tetra-logarithm

if you don't wanna say "heptaconta(70)-exponential", don't worry, humanity probably won't ever get thereBig Grin

or

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.

so that for kouznetsov, we can have the mapping information under the iter operator. (it will look a bit like the limit operator)
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RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/10/2009, 05:09 PM

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