Are there functions(or category of functions) S and U such that

$S(T(U(k))) = T(k)$ for any function T where

$S(T(U(k))) \neq U(T(S(k)))$ and, S and U are not identity functions i.e $S(x) \neq x$ and $U(x) \neq x$.

  • $\begingroup$ Is $S\circ T\circ U=T$ supposed to hold for all $T$ such that $S\circ T\circ U\neq U\circ T\circ S$, or just one such $T$? $\endgroup$ – Eric Wofsey Feb 9 '18 at 5:55
  • $\begingroup$ @EricWofsey Ideally for all T, but is there a solution for just one T? $\endgroup$ – Meekaa Saangoo Feb 9 '18 at 10:59

No. Assume that $S(x) \ne x$ for some specific value $x$, and take $T$ to be the constant function $T \equiv x$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.