Hi, infinite-set readers. Set theory is back.
The previous post is on this link. Please read in advance to easily understand this post. Today we will discuss about the addition operation on natural numbers. Happy reading.
The consequence of the Finite Recursion Theorem raises a theorem. The theorem is also called Finite Recursion Theorem because the same in the rationale.
Theorem : (Finite Recursion Theorem)
Given any and the function , then there is a single function such that :
Based on the above hypothesis, it can be formed :
with is fuction from to . Obtained, is a binary predicate. With the previous proof of Finite Recursion Theorem in the previous post, then this theorem is proved.
(x) Theorem :
For any there is a single function such that :