continuous function

American  

noun

Mathematics.

1. (loosely) a mathematical function such that a small change in the independent variable, or point of the domain, produces only a small change in the value of the function.

2. (at a point in its domain) a function that has a limit equal to the value of the function at the point; a function that has the property that for any small number, a second number can be found such that when the distance between any other point in the domain and the given point is less than the second number, the difference in the functional values at the two points is less than the first number in absolute value.

3. (at a point in a topological space) a function having the property that for any open set containing the image of the point, an open set about the given point can be found such that the image of the set is contained in the first open set.

4. (on a set in the domain of the function or in a topological space) a function that is continuous at every point of the set.

---

Example Sentences

Figure 1 Temperature as a function of time forms a continuous function.

From Textbooks • Dec. 1, 2021

Since x is a continuous function at x = 5,

From Textbooks • Mar. 30, 2016

Specifically, it guarantees that any continuous function has an antiderivative.

From Textbooks • Mar. 30, 2016

Note that we are using a continuous function to model what is inherently discrete behavior.

From Textbooks • Mar. 30, 2016

The principal properties of a continuous function are: 1.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" by Various