Finding the cardinality of a set where $x$ is greater than $1$ Let $A = {2x : x ∈ Z, -16 <= x <= 4}$.
What is the cardinality of this set?
What would be the translation of this to plain english?
 A: Cardinality is in layman's term the size of the set. For the set $A = \left\{ 2x : x \in \mathbb{Z} , -16 \leq x \leq 4 \right\}$ we can simply list out all the elements explicitly, we have that
$$A = \left\{ -32 , -30, -28, -26, -24, -22, -20, -18, -16, -14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8 \right\}$$
Counting the number of elements we find out that the cardinality of the set is $21$.
A: The cardinality is the amount of elements in a given set. 
For your set, $A = \left\{2x:x\in \mathbb{Z},-16\leq x\leq4\right\}$, $x$ takes on integer values between $-16$ and $4$.
Note $2x$ is the condition that defines each element of the set, given some $x$ in the bounded interval $[-16,4]$. Therefore, for each input $x$, you get a corresponding mapping/output $2x$.
So, the cardinality is simply the amount of countable integers in the bounded interval $[-16,4]$
We note $x$ can take on values of: $-16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4$
So, the cardinality is $21$.
Note, to obtain the actual set, simply multiply each $x$ input by $2$.
