Sets

When shopping for laptops online, have you ever filtered by brand or price range? When you do that, you create a collection of laptops that match your selected filter.

In math, this kind of collection is called a set. A set is a well-defined collection of distinct objects, and each object is called an element.

There are two ways to write a set. One way is the roster method, where we list each element inside curly braces. For example, if you filter laptops by brand, you might see a list of brands. As a set, it can be written as {Dell, Lenovo, HP, Apple}.

When writing a set, the order of the elements does not matter. As long as a set contains the same elements, it is the same set.

But when a set is too large to list or is defined by a rule, we use the set-builder method. This method uses a variable to represent the elements and a rule to define the set. For example, if you filter laptops under $800, you can use x to represent any laptop, and the rule “priced under $800” to specify which laptops belong to the set.

So, whether we list the elements or use a rule, a set helps us clearly show which elements belong.