13.1 Three-Dimensional Coordinate Systems

 

Cartesian Products

The Cartesian product RxR is the set of all ordered pairs of real numbers and is denoted by R².

 

RxR = { (x, y) | x, y ε R }

 

The Cartesian product RxRxR is the set of all ordered triples of real numbers and is denoted by R³.

 

RxRxR = { (x, y, z) | x, y, z ε R }

 

There is a one-to-one correspondence between the points in space and the ordered triples in R³.

It is called a three-dimensional rectangular coordinate system.

The three coordinate axes divide space into eight regions called octants, and the first octant is the set of points whose coordinates are all positive.

 

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