How should I read and interpret $A = \{\,n^2 + 2 \mid n \in \mathbb{Z} \text{ is an odd integer}\,\}$ As my question states, I need to interpret: $A = \{\,n^2 + 2 \mid n  \in \mathbb{Z} \text{ is an odd integer}\,\}$
Does this mean that any odd integer $n$ will work, or does this mean that the output of $n^2 + 2$ must be an odd integer?
For example, would these numbers be in the set: $\{1,3,5,7,\ldots\}$ or would $5$ not be in the set because $2^2 + 2 = 6$? 

Unfortunately, no, any odd integer $n$ will not work. 
The set A should be interpreted as (with no math symbols) "A is the set containing all elements of the form n squared plus 2, such that n is an odd integer."
This means that anything in the set must be able to be put into the form (an odd integer)$^2 + 2$.
example of the first few terms: 3, 11, 27, 51, etc
