continuous function
In mathematics, a 'continuous function' describes a function that has no abrupt changes or breaks in its graph, essential in analysis and topology.
Definition
C1Mathematical Analysis
(technical, academic)A function where small changes in the input result in small changes in the output, without any abrupt jumps or breaks.
Example
- The graph of a continuous function is smooth and unbroken.
C2Mathematical Analysis
(technical, academic)A function is continuous at a point if the limit of the function as it approaches that point is equal to the function's value at that point.
Example
- A function f(x) is continuous at x=a if lim(x→a) f(x) = f(a).
C2Topology
(technical, academic)A function between two topological spaces where the preimage of any open set is open.
B2General
(informal)A function that can be drawn without lifting the pencil from the paper.
Example
- Visualizing a continuous function is like drawing a smooth curve without any breaks.
Similar
Terms that have similar or relatively close meanings to "continuous function":
monotone functionupper semi-continuousmeasurable functionanalytic functionhomogeneous functiontranscendental function