Question

If $R$ is the set of real numbers, then Cartesian product $R\times R\times R$ represents

• A. coordinates of all points in two dimensional space
• B. coordinates of all points in three dimensional space
• C. Both (a) and (b)
• D. None of the above

Answer 1

Answer: (B)

The Cartesian product $R\times R$ represents the set $R\times R=\{(x,y):x,y\in R\}$, which represents the coordinate of all the point in two dimensional space and the Cartesian product $R\times R\times R$ represents the set $R\times R\times R=\{(x,y,z):x,y,z\in R\}$, which represents the coordinates of all the points in three dimensional space.