Sets are a fundamental concept in the study of Mathematics and Statistics, but it has a vast impact in many fields daily. Sets are usually used to represent, collect and study similar data. Data is an essential aspect of today’s life. Today we are able to observe changes in our daily lives that are driven by the data. The purpose of sets is to house a collection of related objects. They are essential everywhere in mathematics because every field of mathematics uses or refers to sets somehow. They are necessary for building a more complex mathematical structure.
Set theory is critical because it is a theory of integers, infinite ordinals, real numbers, and axiom systems models, all in one consolidated structure. The idea of set theory is to turn logical predictions, like “x is less than 50, and x is greater than 1”, into objects, and good formal rules can manipulate them. Also, we can define subsets based on the requirement. There are many mathematical operations that we can perform on sets. In many areas of mathematics, we use sets to represent different elements.
Apart from the usage of sets in mathematics, we use them in our daily life. Let’s have a look at some examples in our daily existence that represent sets. The kitchen is one of the most relevant examples of sets. Here, we can see the collection of things arranged conveniently and logically. School bags for children are also considered as examples. Other examples may include shopping malls, playlist, rules, universe, representative house, etc. Whenever we visit a shopping mall, we can notice that there will be individual or separate sections for different things. For example, clothing stores are on another floor, the play zone or food court will be at another mall. Similarly, we can observe other things such as toys, electronics and so on.
Every institution, i.e. school, college, university or company, has different sets of rules that every student or employee must follow. Here, rules may be disciplinary rules, hostel rules, rules for leave, timings for classes, meetings, presentations, or other activities. Thus, all different types of rules and practices will be separated from others. On our smartphones and computers, many of us have a distinctive sort of playlist of songs present. Classical songs are usually separated from folk songs or any other genre. Thus, we can say that playlists in our devices also form the example of sets. Our universe is another example of a set representation, sometimes representing a power set, with millions of galaxies present in our world separated from each other by some distance.
From the above examples, we can say that sets are the basic analogy to similar real-life objects and their interrelationships. It might be similar to a few things such as we talk about the pride of lions or human beings as a species. We can categorize anything in this world into specific groups based on some criteria. For example, people who like music, sports, painting, dance and so on will represent a separate set with a certain number of people. That means there can be infinite criteria to group people, objects and other things into distinct groups.