If $\displaystyle A = \{0, {1\over2} , 1, {3\over2} , 2, {5\over2} , 3, {7\over2} , 4, {9\over2} , 5\}$, write down the following set;

$\displaystyle \lbrace2n + 1 \in A : n \in A\rbrace$

The solution is $\displaystyle \{1,2,3,4,5\}$ but I can't get my head round why, could someone please explain this to me?

Cheers.