It is a trivial assertion that the binary operation $g(x,y)\mapsto xy$ is associative and also distributive over the binary operation $f(x,y)\mapsto x+y$. We say that $f\leadsto g$ if this occurs, where all the binary operations in consideration are taken over the reals. The question is to determine whether the longest possible chain of functions $$f_1\leadsto f_2\leadsto f_3\leadsto f_4...$$ is finite.
Asked
Active
Viewed 38 times
1
-
Must the functions $f_i$ all be distinct? – Karl Kroningfeld Jan 27 '14 at 23:49
-
Well, I need something more than a triviality, so yes. – Jan 31 '14 at 00:15
1 Answers
0
With some minor tweaks (work over complexes, etc.) you can get an infinite chain. See: https://arxiv.org/abs/math/0112050.
Aeryk
- 679