Talk:Generating Function for Elementary Symmetric Function/Proof 3

14 Nov 2020 Disclaimer: the existing page (Proof 3) is of unknown origin, I had nothing to do with its creation or any subsequent edits.

A fundamental reference for the topic of generating functions: DONALD E. KNUTH THE ART OF COMPUTER PROGRAMMING THIRD EDITION (1997) Volume 1 / Fundamental Algorithms 1.2.9 GENERATING FUNCTIONS Page 87

A quote from page 87:

"When we discover the solution by any means, however sloppy, we may be able to justify the solution independently ... once such an equation has been found, it is a simple matter to prove it by induction, and we need not even mention that we used generating functions to discover it."

Why is $a_0=1$? Explanation: The "Theorem" defines $a_m=e_m(U)$ and $e_0(U)$ is defined to be $1$ (definition as in the Theorem). The first step checks induction step $m=0$, which is the statement $$a_0 = e_0(U)$$ The "proof" would benefit by following well-established ProofWiki rules for induction proofs (many excellent pages exist). Writing "$a_0=1$" is equivalent to saying it is obvious or trivial, which violates the ProofWiki induction proof rules.--Gbgustafson (talk) 07:49, 14 November 2020 (UTC)

That told me. I really need to improve my skills at writing proofs on this site. --prime mover (talk) 09:28, 14 November 2020 (UTC)