Proof that the superset of a Dedekind infinite set is also Dedekind infinite? How can I prove that any superset of an Dedekind-infinite set is also Dedekind-infinite? Or a link to a proof? Any help would be appreciated.

If $A$ is Dedekind-infinite, then there is some $B\subsetneq A$ and $f\colon A\to B$ which is a bijection.
Let $C\supseteq A$, define $$g(c)=\begin{cases} f(c) & c\in A\\ c & c\notin A\end{cases}$$
Then $g\colon C\to B\cup(C\setminus A)$ is a bijection with a proper subset of $C$.
