I have this kind of problems:

1. Let $\displaystyle A$ be a set so that $\displaystyle card(A) \geq 2$. Show that $\displaystyle Sq(A) \preceq A^\omega$. $\displaystyle A ^\omega$ means funtion $\displaystyle g: \omega \rightarrow A $ and $\displaystyle Sq(A)= \bigcup_{n \in \omega} A^n $ ($\displaystyle A^n$ means funtions $\displaystyle h: n \rightarrow A$).

I know that I have to build injection between those sets, but how to do it?

2. Let's designate $\displaystyle F(A) = \{B \in P(A) \mid B finite\}$. Show that $\displaystyle F(A) \approx A$, when $\displaystyle A$ is infinite.

I know that I have find bijection between those sets, but how to do it in this case?