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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.

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    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.2012-12-09
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    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 example2012-12-09
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    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.2012-12-09
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    hmm ok, can you show if f(x)=root(x+5) + 5 is mu-partial recursive? step by step2012-12-09
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    Exactly what definition you want to verify?2012-12-09
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    its simple: Just explain if the function f(x)=root(x+5)+5 is mu-partial recurisve. Argument why it is or why it is not mu-partial recursive. I do not need another definition. I need all those definitions used on a real function, that i have provided here.2012-12-09
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    @Gero: You have not addressed the question of how you are defining recursiveness of real-valued functions. (If you don't know the difference between a real number and a natural number, please go look that up first.) Of course, under any reasonable definition, $x \mapsto \sqrt{x + 5} + 5$ will be recursive, but I must stress _reasonable_.2012-12-09
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    Sorry, we had a misunderstanding. I did not mean real numbers as x element of R, but i meant to use natural numbers instead of variables. can you show if f(x)=root(x+5) + 5 is mu-partial recursive? step by step. Lets assume it is a question in a math test.2012-12-09
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    @Gero: You have just [asked this question on cstheory](http://cstheory.stackexchange.com/q/14676). Please don't cross-post. If you don't get adequate answers on one cite, request migration to another.2012-12-09
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    Ok. I was just stunned that nobody could answer such an easy question/function if f(x)=root(x+5)+5 is mu-partial recursive and why it is mu-partial recursive.2012-12-09

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