Suma de doua functii surjective
Posted: Tue Mar 18, 2008 8:00 pm
Aratati ca orice functie de la \( \mathbb{Z} \) in \( \mathbb{Z} \) se poate scrie ca suma a doua functii surjective.
Scriem \( f=g+h \) cu \( g \) si \( h \) surjective.
Fie \( g(2p)=p \), \( h(2p)=f(2p)-p \) si \( h(2p+1)=p \), \( g(2p+1)=f(2p+1)-p \).
Evident g si h sunt surjective!