Activity for Prime Mover‭

Type	On...	Excerpt	Status	Date
Comment	Post #286572	Added as suggested (more)	—	almost 3 years ago
Edit	Post #286572	Post edited: added definition of entropic structure	—	almost 3 years ago
Edit	Post #286572	Initial revision	—	almost 3 years ago
Question	—	Endomorphisms on an entropic structure whose pointwise product is the identity automorphism - entropic idempotent structure? Context: self-study from Warner's "Modern Algebra (1965): Exercise 16.27. >Let $\alpha$ and $\beta$ be endomorphisms of an entropic structure $(S,\odot )$ such that $\alpha \odot \beta$ is the identity automorphism, and let $\otimes$ be the operation on $S$ defined by: $$x \otimes y = \alpha (x) ... (more)	—	almost 3 years ago
Edit	Post #286571	Post edited:	—	almost 3 years ago
Edit	Post #286571	Initial revision	—	almost 3 years ago
Answer	—	A: In "if and only if" proofs, why's 1 direction easier to prove than the other? Here's a good one: Every set is well-orderable iff the Axiom of Choice holds. It is quite challenging to prove that the Axiom of Choice implies that every set is well-orderable. Smullyan and Fitting build up to it in a focused but leisurely manner over the course of 3 chapters in their "Set Theory... (more)	—	almost 3 years ago