Explanation:
A set of points extending infinitely in all directions on the same flat surface is called a plane. A plane is a two-dimensional flat surface that extends infinitely in all directions. It is an abstract concept that does not have any thickness or depth.

Examples of Planes:
Some examples of planes include a sheet of paper, a tabletop, a blackboard, or a computer screen. These are all flat surfaces that extend infinitely in all directions.

Characteristics of Planes:
Some characteristics of planes include:

- A plane is a two-dimensional surface that has length and width but no depth.
- A plane extends infinitely in all directions.
- A plane is flat, which means that it has no curves or bends.
- A plane is a geometric concept that can be used to help describe and solve mathematical problems.

Uses of Planes:
Planes have many uses in mathematics, science, and engineering. For example:

- In geometry, planes can be used to describe the position and movement of points, lines, and other geometric shapes.
- In physics, planes can be used to describe the behavior of waves and particles.
- In engineering, planes can be used to design and analyze structures such as buildings, bridges, and airplanes.
- In computer graphics, planes can be used to create 2D images and animations.

In Conclusion:
In summary, a plane is a two-dimensional flat surface that extends infinitely in all directions. It is an abstract concept that has many uses in mathematics, science, and engineering.

As we know that a plane is made of the group of lines and a line is made up of a group of points. 

So, plane is made up of a set of points extending infinitely in all directions on same flat surface.

Hence, the answer is plane.