In mathematics, a set is nothing more than the collection of elements considered as an object. Sets are a primitive concept, this means that it is not possible to define them in terms of more elementary notions and their study is carried out informally, appealing to logic and intuition.
It is also a fundamental concept of mathematics, since they allow the formulation of the rest of the mathematical objects such as numbers and functions. It is usually defined by a property that all its elements have in common. This means that a set is defined only by the elements that make it up and by nothing else.
In a nutshell, a set can be written as a list of elements, but without changing the order in the list or adding elements that may be repeated. Sets can be infinite or finite.
The set of natural numbers is infinite, but the set of colors of the rainbow is finite. Sets can be combined by operations, similar to operations on numbers.
Subsets occur when all elements of one set belong to another set. For example, if we have a set made up of red fruits and one of orange fruits, these will be subsets of the set of fruits, because they share the main characteristic of being fruits.
This means that the main set – that of the fruit – has within it subsets: the subset of red fruits and the subset of yellow fruits. This concept is often applied to sets that contain many elements that can be grouped based on other characteristics that they share with each other.
Difference Between Set and Subset
- A set is a grouping of elements that share a common characteristic. A subset is formed from a set and is nothing more than the grouping of certain elements that make up a set, but share another characteristic in common.
- That is, the elements of a subset all belong to a set.