The covering number is a concept in mathematics, particularly in the field of geometry and topology. It refers to the smallest number of sets, often called "covers," needed to completely cover a given space or object. For example, if you have a shape like a circle, the covering number would indicate how many smaller circles are required to cover it entirely without leaving any gaps. In more technical terms, the covering number can be applied to various mathematical structures, such as metric spaces or topological spaces. It helps in understanding the properties of these spaces by analyzing how they can be approximated or represented using simpler shapes or sets.