The Notion of Distance

Some of these contexts are:

• the distance between two real numbers.
• the distance between two points in the plane.
• the distance between two complex numbers.
• the distance between two points in space.
• the distance between two functions on the interval a <= x <= b.

For every context in which the notion of distance is available it is possible to discuss limits.

Because there are so many different contexts we may save time by understanding two things:

1. Some rules about distance appear in every context.

2. It is possible to define limit in a manner that does not depend on the particular context.