In mathematics, a set is simply a collection of distinct objects. Think of it like a bag of your favorite fruits. Inside the bag, you might have an apple, a banana, and an orange. That collection of fruits is a set.

The objects inside a set are called its elements. In our fruit example, the apple is an element, the banana is an element, and the orange is an element.

Two simple rules govern sets. First, the order of elements doesn't matter. A set with {apple, banana} is exactly the same as a set with {banana, apple}. Second, elements cannot be repeated. A set of letters in the word "book" would be {b, o, k}, not {b, o, o, k}.

We write sets by listing their elements between curly braces {}. Each element is separated by a comma.

For example, the set of primary colors can be written as: {red, yellow, blue}

The set of the first five positive whole numbers is: {1, 2, 3, 4, 5}

The diagram above shows a set named $A$. The elements inside the blue boundary, like 3 and 'q', belong to the set. The elements outside, like 5, do not.

To say that an object is an element of a set, we use the symbol $\in$. It looks like a stretched-out letter 'e'. You can read it as "is in" or "is an element of."

If an object is not an element of a set, we use the same symbol with a slash through it: $\notin$. You can read this as "is not in" or "is not an element of."

Let's use an example. Suppose we have a set $V$ which contains the vowels of the English alphabet:

$V = \{a, e, i, o, u\}$

We can say that 'a' is an element of this set: $a \in V$

But the letter 'b' is not a vowel, so it's not in the set: $b \notin V$

That's the basic idea. A set is a simple, powerful tool for grouping things in mathematics.