continuity

continuity

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In mathematics,

continuity

Is a property of a function. Intuitively speaking, a continuous function is a function that when the change of input value is small enough, the change of output will be small enough. If a slight change in the input value results in a sudden jump in the output value, even if it cannot be defined, then this function is called "yes"

Discontinuity

A function with

Discontinuity

）。

The most fundamental definition of continuity is in topology, which will be discussed in detail in term continuous function (topology). In order theory, especially in domain theory, there is another Abstract continuity derived from this basic concept: Scott continuity.

Real valued continuous function

The most basic and common continuous functions are those whose domain is a subset of the real number set and whose value is also a real number. For example, the height of the flower mentioned above belongs to this type. The continuity of this kind of function can be represented by the image in rectangular coordinate system. Such a function is continuous, if roughly speaking, its image is a single unbreakable curve, and there is no curve

interrupted

、

jump

or

Oscillation of infinite approximation

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