The concept of size is often applied to ideas that have no physical reality. In mathematics, magnitude is the size of a mathematical object, which is an abstract object with no concrete existence. Magnitude is a property by which the object can be compared as larger or smaller than other objects of the same kind. More formally, an object's magnitude is an ordering (or ranking) of the class of objects to which it belongs. There are various other mathematical concepts of size for sets, such as: