How to show if a function is partial recursive?

I have seen and understood the most definitions but i just could not understand how to show if a function is mu-partial recursive or not. I used search engines, but all I find are just more lectures with definitions...

Lets say I have a function like

f(x) = x^2


or

f(x)=root(x+5) + 5


Can you proof if those functions are mu-partial recursive? Explain why this function is mu-partial recurisve.

-
show that x is partial recursive and the product of two partial recursive is partial recursive. Then show the sum of two partial recursive is partial recursive, and show root is partial recursive. –  user51427 Dec 9 '12 at 0:33
Thx for comment!! but this is right now to difficult for me. I see all the definitions with variables, but i need one real example with real numbers :/. Something like a cookbook example –  Gero Dec 9 '12 at 0:35
Recursive functions are, officially, only defined on natural numbers. You'll have to be more precise about what you mean by a recursive real-valued function. –  Zhen Lin Dec 9 '12 at 0:37
hmm ok, can you show if f(x)=root(x+5) + 5 is mu-partial recursive? step by step –  Gero Dec 9 '12 at 0:39
Exactly what definition you want to verify? –  Berci Dec 9 '12 at 3:02
show 5 more comments

1 Answer

I'm not sure what type of answer you're supposed to give, but partial recursive functions correspond to all computable functions. Thus, if you can write a computer program to represent the function, it's partial recursive. Either that or you can start from the definitions and build up to the functions you are given. In this case, both of your examples are clearly partial-recursive.

-
your answer is just once again another definition. I have a specific case and i am interested in an specific answer to the function f(x)=root(x+5)+5 –  Gero Dec 9 '12 at 9:36
I know it's a definition, but using the definition and some thinking will allow you to come up with an answer. Plus, I told you the answer. –  gvv Dec 11 '12 at 21:36
add comment