Trouble with chessboard set definition

Question

The following equation is supposed to define a set of points that produces a square grid (like a chessboard).

s is the distance between each square in the grid w and h are the dimensions of the board overall

My question is, does the dot following (x,y,0) mean multiply? If so this would produce an infinite amount of points greater than 1 and up until w,h, which isn’t a grid. I’m guessing it doesn’t mean multiply in this context and means something else, if so, what does it mean?

Any help with this would be greatly appreciated

Answer 1

I think what you want is $$ \{ s(x,y,0) \ | \ x, y \in \mathbb{Z} \text{ and } \ 0 \le x < w, \ 0 \le y < h \} $$ For $s=1.5, h=2, w = 3$ that produces the grid of points

(0,1.5,0)  (1.5,1.5,0)  (3,1.5,0) 



(0,  0,0)  (1.5,  0,0)  (3,  0,0)