I'm trying to do exercise 7.11 of Jech's "Set Theory": If $D$ and $E$ are ultrafilters on $\omega$, then $D\leq E$ and $E\leq D$ implies that $D\equiv E$, where $\leq$ is the Rudin-Keisler ordering, and in this book is defined $D\equiv E$ iff there exists a bijection $f:\omega\rightarrow\omega$ such that $f(D)=E$, there exists a previous result in which one proves that :
- if $f:\omega\rightarrow\omega$ is such that $f(D)=D$, then $\{n:f(n)=n\}\in D$.
I also read this definition in wikipedia, under this definition the problem is trivial because of $1$, but I do not know how to proceed under Jech's definition, any help will be appreciated.