This is meant as a note. I will definitely expand this article later. I hope this method has not been discovered before :(. Say is a recursion relation. Then is the intersection point of and . For example, if we have , then is the y-coordinate of the intersection of and .
Edit: After reading proofs of this theorem, it seems to me that this is similar in spirit to an already established proof (Proof 2 on ProofWiki, for instance). This is a constructive proof of Hilbert’s Basis Theorem. Hilbert’s Basis Theorem says that if is a Noetherian ring (every ideal has a finite number of generators), thenContinue reading “Original, constructive proof of Hilbert’s Basis Theorem.”