The Notion of Distance
We wish to be able to discuss distance in various contexts.
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:
- Some rules about distance
appear in every context.
- It is possible to define limit
in a manner that does not depend on the particular context.