Endpoint and singularity are different mathematical concepts. Endpoint refers to the point on the boundary of function definition domain, which can be a closed interval or an open interval; Singularity means that a function cannot be defined or continuous at a certain point.

In mathematics, the endpoint of a function refers to a point on the boundary of a function domain. Singularity means that a function cannot be defined or continuous at a certain point.

First, let's discuss endpoints. When we discuss the domain of a function, we usually pay attention to its left end and right end. The left end point is the minimum value of the function domain and the beginning of the domain. The endpoint on the right is the maximum value of the function domain and the end point of the domain.

The endpoint of a function may or may not be included in its domain. When the endpoint of a function is contained in its domain, we call it a closed interval, and the function value at the endpoint is defined. When the endpoint of a function is not within its definition domain, we call it an open interval, and the function value at the endpoint may not exist or cannot be defined.

An endpoint is a point on the boundary of a function domain, which can be a part of a closed interval or an open interval. Singularity means that a function cannot be defined or continuous at a certain point.

Next, let's discuss singularities. Singularity means that a function cannot be defined or continuous at a certain point. The existence of singularity means that the function is not clearly defined or can not be continuous in a certain range near this point. Singularity can be a point within the domain of function or a point outside the domain of function.

So endpoint and singularity are different concepts. An endpoint is a point on the boundary of a function domain, which can be a part of a closed interval or an open interval. Singularity means that a function cannot be defined or continuous at a certain point.

It should be noted that we are talking about ordinary mathematical functions. In more advanced mathematical fields, such as complex function theory or curve theory, the definition and characteristics of singularities may be different. In these cases, the domain and nature of the function may be more complex, and more types of singularities may appear.