08/10/2009, 05:09 PM
(This post was last modified: 08/10/2009, 05:57 PM by Base-Acid Tetration.)

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 there

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)

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 there

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)