12/14/2012, 05:06 PM
Half-iterate can only be defined if we define someting in third hyper operation called "power level".
because we always assume these levels as integers
for example 2^x , 2^2^x , etc..
in the example, number 2 is powered to the first power level and also to the second power level.
but we shall study it also to non-integers level.
this study must be related to third hyper operation (the exponential function) before we jump to fourth hyper opertation (tetration).
if we can find solutions for that, it means half-itrated could be defined.
for me it is clear that:
(n^^x)^(*)(n^^x) = x , while * means "to the half power level"
because we always assume these levels as integers
for example 2^x , 2^2^x , etc..
in the example, number 2 is powered to the first power level and also to the second power level.
but we shall study it also to non-integers level.
this study must be related to third hyper operation (the exponential function) before we jump to fourth hyper opertation (tetration).
if we can find solutions for that, it means half-itrated could be defined.
for me it is clear that:
(n^^x)^(*)(n^^x) = x , while * means "to the half power level"
