We define and learn how to plot points in .

RRN-0010: A Brief Introduction to

The set of all real numbers is denoted by . It is convenient to associate real numbers with points on a line, called the real number line.

The set of all ordered pairs , where and are real numbers is called . Using set notation we write: Geometrically speaking, can be associated with a coordinate plane in which we refer to each point by its and coordinates.

The set of all ordered triples , where , and are real numbers, is called . Geometrically, points of are associated with points of a three-dimensional space whose position is given by their , and coordinates.

Each pair of axes in determines a plane. The resulting three planes are called coordinate planes. Each coordinate plane is named after the axes that determine it. Thus, we have the -plane, -plane, and -plane. Coordinate planes intersect at the point , called the origin, and subdivide into eight regions, called octants.

The set of all ordered -tuples , where is a real number for is called . The point in is called the origin.

cannot be visualized for , but many familiar ideas, such as the distance formula, can be generalized to .

Practice Problems

Find the coordinates of each point.