What does the Comp function mean?

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Discussion Overview

The discussion revolves around the interpretation of a specific function presented in a proof related to Ackermann's function, particularly focusing on the meaning of its parameters and whether it can be classified as a composite function or related to primitive recursive functions. The scope includes theoretical exploration and clarification of concepts in mathematical logic.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks clarification on the meaning of a function with specific parameters as seen in a proof related to Ackermann's function.
  • Another participant proposes that the function might indicate "composite," suggesting that Ackermann's function is not primitive recursive, thus implying it must be composite.
  • There is a question about the significance of the parameter "p11" within the function, indicating uncertainty about its role.
  • Some participants speculate that "p11" could represent one of the primitive recursive functions or a general form of such functions, though this is not confirmed.

Areas of Agreement / Disagreement

Participants express differing interpretations regarding the meaning of the function and its parameters, with no consensus reached on the exact nature of "p11" or the classification of the function as composite or primitive recursive.

Contextual Notes

There are unresolved questions regarding the definitions and implications of the terms used, particularly concerning the classification of functions and the specific parameters involved.

japplepie
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I've been looking at this proof -> http://basics.sjtu.edu.cn/~liguoqiang/teaching/comp14/materials/Ackermann.pdf
At the bottom of the second page, there is this thing which looks like this:
http://s24.postimg.org/sxtz7pef9/what.png

Could someone please explain what that function with those weird parameters mean please, thank you :)
 
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jedishrfu said:
My guess is it means composite. The proof is trying to demonstrate the Ackermann's function is not a primitive recursive function (Pr) so that means it must be a composite function.

http://en.wikipedia.org/wiki/Primitive_recursive_function
I see, but what is the p11 in the parameter?
 
Could that be one of the primitive recursive functions?
 
jedishrfu said:
Could that be one of the primitive recursive functions?
I think what it means is the general form of the any kind of primitive recursive function, but I'm not sure.. What do you think?
 

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