11/23/2011, 06:00 PM
as the title says , i object to linear interpretations of the superfunctionoperator.
why ?
first reason is that it isnt always true.
second reason is i dont know when it applies and when not , or in other words how many exceptions there are.
the following example should clarify my objections :
to compute the inversesuperoperation once we take
g(x) is inverse super of f(x)
f( inv.f(x)+1) = g(x)
so ; the inverse of exp(x) is e*x.
the inverse of e*x is x+e
the inverse of x+e is x+1
the inverse of x+1 is x+1
the inverse of x+1 is x+1
the inverse of x+1 is x+1
...
see , we have an annoying fixed point like function that is irreversibel and we lost all information of the original function in the process.
the super of x+1 could be any x + c.
if we call x + c the 0th super , then there are no NEGATIVE supers.
so the kth integer super is in trouble for negative integers and hence so is substracting anything too large from any finite k.
another remark is that most superfunctions are periodic or quasi-periodic.
also most superfunctions have branches , which is hard to " half anything with ".
and as asked before , what does the converging ooth super look like ?
like i said , i dont know how many exceptions there are ...
are there other functions apart from non-negative k superth of x + c that also lead to a paradox or fixed points ?
what functions cycle under the superfunction operator ?
just some remarks
regards
tommy1729
why ?
first reason is that it isnt always true.
second reason is i dont know when it applies and when not , or in other words how many exceptions there are.
the following example should clarify my objections :
to compute the inversesuperoperation once we take
g(x) is inverse super of f(x)
f( inv.f(x)+1) = g(x)
so ; the inverse of exp(x) is e*x.
the inverse of e*x is x+e
the inverse of x+e is x+1
the inverse of x+1 is x+1
the inverse of x+1 is x+1
the inverse of x+1 is x+1
...
see , we have an annoying fixed point like function that is irreversibel and we lost all information of the original function in the process.
the super of x+1 could be any x + c.
if we call x + c the 0th super , then there are no NEGATIVE supers.
so the kth integer super is in trouble for negative integers and hence so is substracting anything too large from any finite k.
another remark is that most superfunctions are periodic or quasi-periodic.
also most superfunctions have branches , which is hard to " half anything with ".
and as asked before , what does the converging ooth super look like ?
like i said , i dont know how many exceptions there are ...
are there other functions apart from non-negative k superth of x + c that also lead to a paradox or fixed points ?
what functions cycle under the superfunction operator ?
just some remarks
regards
tommy1729