What means a set in $Z^2$?

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I was reading a text when I noticed this:

"... let B $\subset$ $Z^2$ be the set..."

What I suppose is that B is a set wich contains integer values in $\mathbb{R}^2$, but I've never seen such symbol. Is it correct?

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2 Answers

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$\Bbb Z^2$ is standard notation for the Cartesian square of the Integers; the set of all pairs of integers.

$$\Bbb Z^2=\{(x,y): x\in \Bbb Z, y\in\Bbb Z\}$$

If $B$ is a proper subset of this, which is what $B\subset \Bbb Z^2$ means, then $B$ is some set whose elements are pairs of integers.

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Without any further context I would guess $\mathbb{Z}^2=\mathbb{Z}\times \mathbb{Z}=\{(a,b) \mid a,b \in \mathbb{Z} \}$.

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