Continuous function ↩

shorthands: {}
aliases: [continuous function, Continuous, continuous]
created: 2021-10-18 16:16:49
modified: 2022-06-15 01:21:12

Intuitively

A function that does not have any abrupt changes in value, known as discontinuities.

Definition

Let be a function defined on a subset of real numbers. can be , or any closed or open interval.

Definition in terms of limits of functions

is continuous in if:

Definition in terms of neighborhoods

is continuous in if:

for any neighborhood there is a neighborhood in its domain such that whenever .

Generalization in metric spaces

Continuity can be generalized for metric spaces, see continuous mapping.