03/15/2011, 10:49 PM

(03/15/2011, 10:22 PM)tommy1729 Wrote: if i understand this confusing thread well

x {0.5} x = x !

in fact x {y} x = x

at least following from

( quote )

In other words, for a {0.25} b, with a<b,

m1 of a and b = a + (b-a)*0.25 (0.25 of the way between a and b, judged arithmetically)

m2 of a and b = a * (b/a)^0.25 (0.25 of the way between a and b, judged geometrically)

Now plug m1 and m2 into a and b, and iterate until you get something stable (i.e. m1 = m2 to whatever degree of precision you need)

( end quote )

unless you guys started using different ideas since the time of the quote.

furthermore i think this has nothing to do with * tetration * and see it more like an idea inspired by Gauss Aritmetic-Geometric Mean.

If this was not my favorite forum and due to the lack of good math forums in general imho , i might not have read it in the first place ( OP was already unaware of Gauss AGM Mean ) although it might get intresting soon ...

i would be more carefull to associate this immediately with a new * slog *.

i think JmsNxn is a bit overenthousiastic.

maybe its me , but the only intresting thing i can see at the moment is :

does this ' new ' mean have a closed form similar to gauss his result ?

( i assume its analytic ?? for complex z_i : z1 {z2} z3 ? )

furthermore , i have no idea why JmsNxn thinks x {1.5} 2 = x {0.5} x

???

tommy1729

I thought the identity function would have been stable. And if it was, it would've been possible to create a variant of tetration. Solving semi-operators can solve tetration.

and

x {1.5} 2 = x {0.5} x

the same way x * 2 = x + x,

and x ^ 2 = x * x

The law of recursion must hold.