Imagine the confusion in our lives if it wasn’t possible for us to organize things. One of the key aspects of organizing is creating sets of similar objects or items and putting them together in one place. This brings us to today’s topic of discussion – Sets and their application in our lives. Students get to learn set theory in sixth to eighth-grade math curricula.
Many of them may question the importance of learning this topic and wonder if these theories have any actual application in our lives. In order to disperse your confusion and boost your confidence in mathematics, we have curated this article wherein you’ll get to learn the basics of set theory, its relevance in our lives, and some real-life examples to show that sets are indeed important.
So, what makes a set?
A set is a group or a collection of well-defined and similar objects. Each object is known as the “element” of the group. Interestingly, there isn’t any limit to how many elements can make a set. You can have none, one, two, or many!
Mathematically, a set is written as:
A = {2, 4, 6, 8, 10}
Here, A denotes the name of the set, which contains five elements – 2, 4, 6, 8, and 10. One thing you must note here is the use of brackets. We always use curly brackets to represent a set.
In addition, sets are not just of one type. Depending on what it encompasses, a set is classified into empty, singleton, finite, and infinite sets. Furthermore, depending on how sets stand in comparison to each other, they are classified as equal sets, equivalent sets, disjoint sets, subsets, supersets, and universal sets.
Relevance of sets in our day-to-day life
Set theory is a fundamental concept of mathematics. It is the foundation of several other topics, such as statistics and probability, and so on. Besides being a crucial part of complex mathematical subjects, set theory is equally important to make our lives less chaotic and more orderly.
Although we never realize we are applying the concept of sets in our day-to-day life, we surely do. While applying our organizational skills, right from arranging our bags before we go to school to tidying up our room every day, we apply the concept of sets to keep things organized. The social circles we belong to are also sets of people with similar interests and ideologies. And data sets used for analysis enable us to draw conclusions and make informed decisions.
Real-world sets we come across regularly
1. Kitchen sets
The kitchen is that place of the house where you can find numerous kinds of sets. You must have seen your mom organizing each kitchen cabinet with one particular item. There are sets of plates, bowls, glasses, cooking utensils, tableware, and many other things that are arranged as sets in the kitchen. Applying this mathematical concept in this part of the household ensures everything is organized, and you don’t have a tough time finding what you need.
2. School rules
Every school, or even a workplace, has some rules which students and workers must follow on any given day. These rules are a set of well-defined statements that tell people what they are and aren’t allowed to do. Rules keep everything running smoothly during school and work hours, ensuring discipline and safety. We have rules for different scenarios, for example, home rules, classroom rules, playground rules, etc., and each one is a different set from the others.
3. Your favorite playlist
We’re sure you must be having a playlist on your cell phone with all your favorites. Right? This playlist is also a set of songs that you especially like. Each of your friends or your family members must be having their own playlists with their favorite songs to listen to. Here, each playlist is an individual set. It could be, however, possible that some elements in your set of favorite songs are also a part of your friend’s favorites, making them what we call “overlapping sets.”
4. Grade-level school books
Each grade level has a fixed curriculum to follow, so the books for each grade level are also different. Books suitable for each grade level make a distinct set. For instance, students in grade 5 use a set of books that cover the topics to be studied in grade 5. The same is the case with other grades as well. Students must, therefore, study the recommended set of books according to their class rather than those belonging to another grade level.
5. Closet
A closet is another household space where you can find sets of different kinds. You must have seen how a closet is divided into separate sections where one can store various items neatly. There’s space for hangers holding shirts and dresses. Then there are sections for storing sets of jeans, pants, t-shirts, etc. You also have drawers where you can arrange sets of socks, undergarments, and even your accessories.
6. Followers on social media
Social media has become an inseparable part of our lives in today’s times. Almost every person now has a social media account. Your friends on Facebook, followers on Instagram, or any other social platform are good examples of sets. As a matter of fact, every account has its own set of followers and friends, which belong to the larger set encompassing all users of that social media platform.
7. Weekly grocery
Ask your parents to show you the weekly grocery list. You will notice that the list contains several items you can further segregate into multiple groups, such as fruits, dairy, meats, veggies, snacks, etc. Here, the entire grocery list is one set which we can call “the universal set,” and the individual groups of items are subsets of the universal set.
8. Shopping store
A shopping store is another excellent example where the application of sets is very prominent. Enter a store, and you will find sections or rather sets where specific items are displayed. There’s a clothing section, a footwear section, a handbag section, and so much more. Each section implies a set which has a limited number of elements. And all elements within one set belong to a specific category of items.
9. Months in a year
January, February, March, and so on. All the months in a year also make up a set with twelve elements. The “months of the year” set can be described as a finite set because it has a fixed number of elements that one can count easily. Along similar lines, one week is also a set of seven days, namely Monday, Tuesday, and so on, and a year is a set of 365 days.
10. Sports teams
A tournament is a competition between numerous teams. And each team participating in the tournament is a set of players representing a particular state or country. So, the next time you see soccer or baseball, be aware that the two teams fighting against each other are also real-life examples of sets.
In Summary,
Apart from the ones stated above, we have other examples, like a jewelry box, a makeup kit, a restaurant’s menu, or even the universe, which show how sets are a part of our lives. After looking at all the examples mentioned above, we hope you are convinced about how sets make our lives systematic and organized.
Without the existence of set theory, we would have had poor structure and organization, and it would have been arduous for us to simplify things. In essence, sets serve as fundamental tools for classifying and understanding the world around us, contributing to our efficiency, decision-making, and overall life experience.
An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,