Cartesian product of a set Question:
What is A $\times$ A , where A = {0, $\pm$1, $\pm$2, ...} ?
Thinking:
Is this a set say B = {0, 1, 2, ... } ? 
This was in my homework can you help me ?

No, $A\times A$ is not a sequence. Neither is $A$: it’s just a set.
By definition $A\times A=\{\langle a_1,a_2\rangle:a_1,a_2\in A\}$. Thus, $A\times A$ contains elements like $\langle 1,0\rangle$, $\langle -2,17\rangle$, and so on. Indeed, since $A$ is just the set of all integers, usually denoted by $\Bbb Z$, $A\times A$ is simply the set of all ordered pairs of integers. Here is a picture of $A\times A$: the lines are the coordinate axes, and the dots are the points of $A\times A$, thought of as points in the plane.

