\(RR^{3}\) is the three dimensional coordinate system which contains x, y, and z-coordinates.

The equation \(z \geq -1\ in\ RR^{3}\)

represents the set \({(x, y, z)|z \geq-1},\)

which is the set of all points in \(RR^{3}\) whose z-coordinate is greater than or equal to 8 and x, y-coordinates are any values.

The equation \(z = -1\) is sketched as shown below in Figure 1.

Thus, the equation \(z \geq -1\ in\ RR^{3}\)

represents a half-space that consists of all points which are on or above the plane \(z = -1.\)

The equation \(z \geq -1\ in\ RR^{3}\)

represents the set \({(x, y, z)|z \geq-1},\)

which is the set of all points in \(RR^{3}\) whose z-coordinate is greater than or equal to 8 and x, y-coordinates are any values.

The equation \(z = -1\) is sketched as shown below in Figure 1.

Thus, the equation \(z \geq -1\ in\ RR^{3}\)

represents a half-space that consists of all points which are on or above the plane \(z = -1.\)