andydude Wrote:First, you do a very poor job of explaining yourself, so I'm not sure if I (or anyone on the math forum) have completely understood your algorithm.
there is nothing wrong with what i said.
i defined f(x) as the limit n -> oo in
f(f(x)) = exp(x) - exp( -1 * 25^n * x^2 )
note that f(x) can be easily computed because f(0) = 0
like i already said in the original post.
you know how to solve f(f(x)) = exp(x) - 1
then you can use the same method for
f(f(x)) = exp(x) - exp( -1 * 25^n * x^2 )
Quote: I am very interested in your algorithm, but you have not shown enough of it for me to duplicate your results, or verify your solution.
yes i have !
take the limit n -> oo.
think in terms of taylor series !
my limit n-> oo gives a taylor series for f(f(x)) = exp(x).
Quote:Until I can verify how your definition of f(x) is a solution to this equation, I'm not sure if you have a solution at all. I recommend you explain more about why you think it is a solution, rather than listing examples.
Second, f(f(x)) = exp(x) has already been solved.
no , it was not solved before , thats part of why this forum exists.
im talking about taylor series that converge for all reals !
Quote: This is what regular iteration is good at. Simply searching this forum for "regular" will give you many places to start, if you would like to know more. The problem with the solution that regular iteration gives is that it only converges for integer iterates. This means that the power series for f(x) is not analytic, so it cannot be used to find a value, but it may be good for approximations.
im aware of " regular " but my method gives analytic for all real values not just some integers !
Quote:Third, you do not need to include a license. A simple ©2009... will suffice.
Also, none of what you said is part of an "invention" in the technical sense, because you do not make any claims. Basically, you need to tell people what it is before you can say you have an invention. From what you said, I have no idea what you claim to have invented. Did you invent "f" or "g"? Did you invent (25^n)? For all I know you could have just invented the word "greedy". Also, none of this would hold up in the USPTO because you can't patent math. The only way to do something similar is to publish your ideas in a well-known journal, for example, American Mathematical Monthly, or the like.
i know i cannot patent math.
but i can still be the inventor of an idea , an analytic solution to f(f(x)) = exp(x).
compare to : you cant patent the concept or use of " integrals " but you can compute a hard integral that no one else could before you , and you can sell math software and mention that.
and you can object if someone said you he knew it first , while it was yourself.
now , i might sound agressive , but that is not the intention.
i do feel a bit attacked though ...
surely defining a limit is not " something that cannot be checked " ?
Moderator's note: corrected quoting and removed the subsequent post with same content