What is the difference between Godel’s Completeness and Incompleteness Theorems?

They are about different kinds of “completeness”. The Completeness theorem is about the correspondence between “truth” and provability in first order logic. The Incompleteness theorem is about there being either a proof of P or of ¬P for every sentence P in the language.

— Arturo Magidin Dec 17 ’10 at 19:36

— Mathematics – Stack Exchange

2013.10.10 Thursday ACHK