In addition, in the graph theory of discrete mathematics, the definition of an isolated point is a point with infinite correlation.

The following is a graph of isolated points:

First of all, a set must be given, and the isolated point is the critical area where it exists. In this critical area, no point belongs to this set except it.

For example:

A set consists of all integers, so every point in the set is an isolated point. There are no outliers in the set of all rational numbers.

For example, the set {0, 1, 1/2, 1/3, 1/4, ...}, where 0 is not an isolated point, all other points are isolated points. 0 is not an isolated point, because no matter how close to 0, there will always be a1/n.

Extended data:

Discrimination of the difference between gathering points and isolated points in higher mathematics;

Convergence point: If there is a set point in any centripetal neighborhood of this point, then this point is the convergence point.

For example, for any open circle, every point on the corresponding closed circle is its aggregation point (there are points on the circle on the circumference or in the centripetal neighborhood of any point in the circle).

For a closed circle, every point on the closed circle is also its gathering point. But every point outside the circle is neither a gathering point of an open circle nor a gathering point of a closed circle (if the circle is tangent to the original circle with this point as the center, then this centripetal neighborhood does not contain the points of the set, so it is not a gathering point).

Isolated point: a point belonging to a set, but not a gathering point. Let a set be the set of all points with integer coordinates on the coordinate system, then every point on the set is an isolated point, because a circle with a radius of 1 centered on this point does not contain the points of the set, so it is an isolated point.

An isolated point is the existence of a neighborhood. In this range, only it belongs to point set D, and point set D cannot be a regional point set. For example, it is not required that the aggregation point belongs to c, and if it does, it is called a complete point set C.