What does $(x, y)$ $\in [10,-10] \times [0,0]$ mean - Multiple of two domains?

Question

I tried to search online but I can't find the right definition. Does the first square bracket represent the domain of $x$ and the second square bracket the domain of $y$? Therefore:

does $(x, y)$ $ \in [10,-10] \times [0,0] $ mean a line from $(-10,0)$ to $(10,0)$?

The context:

Answer 1

Lets look at the defintion of a Cartesian product of two sets:

Let $A$, $B$ both be sets such that $a \in A$ and $b \in B$. Then the set $A \times B$ $:=${$(a,b) | a \in A, b \in B$} is the cartesian product of the the sets $A$ and $B$. We read this set as "$A$ cross $B$".

Notice in defintion: $a \in A$ in the first slot and $b \in B$ in the second slot of the ordered pairs $(a,b)$ $\in A \times B$. So, for the set you mentioned:

When the author states that $(x,y) \in [10,-10] \times [0,0]$ (which we will assume to be a typo since the interval $[0,0]$ seems a little out of context here; the author probably meant $[10,-10] \times [0,5]$ as the domain) they mean that $x$ can be any value equal to or between $10$ and $-10$ and $y = 0$.

Remark: Note that $[10,-10], [0,0] \subset \mathbb{R}$ and $[10,-10] \times [0,0] \subset \mathbb{R}^2$. For a more geometrical interpretation as to why the author chose $[10,-10] \times [0,0]$ as the domain, see NeitherNor's comment.

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EDIT: After thinking more about this problem at a geometric level, $[10,-10] \times [0,0] \subset \mathbb{R}^2$ being the domain is certainly not a typo. As you can see in the graph of the ellipse $\frac{x^{2}}{100}+\frac{y^{2}}{25} = 1$, on $\mathbb{R}^2$, below - the domain is certainly the line $[10,-10] \times [0,0]$ - of course in this problem, we are only studying the upper half of the ellipse.