Empty set facts for kids

The empty set, which means it has nothing inside!

In mathematics, the empty set is a special kind of set that contains absolutely nothing. Think of it like an empty box or an empty basket. It's often shown using symbols like , , or simply as two curly brackets with nothing inside: .

For example, imagine you have a group of integer numbers. Integers are whole numbers like 1, 2, 3, 4, and so on, or -1, -2, -3. Now, let's think about the integers that are between the numbers two and three. Can you name any whole numbers that are bigger than two but smaller than three? There aren't any! So, the set of integers between two and three is an empty set.

What is a Vacuous Truth?

Sometimes, when we talk about the empty set, we come across something called a vacuous truth. This sounds complicated, but it's actually quite simple. A statement about all the things in an empty set is automatically true, even if it seems a bit strange.

Let's use our example again: "All integers between two and three are greater than seven." This statement is true! Why? Because there are no integers between two and three to begin with. Since there are no numbers to check, the statement can't be false. It's true because there's nothing to prove it wrong. This kind of truth is called "vacuous" because it's true due to the lack of anything to contradict it.

Symbols for the Empty Set

The symbol that is often used for the empty set comes from the Latin letter Ø. It's not the same as the Greek letter φ, even though they might look a bit similar. The empty set is also sometimes called the null set. Both names mean the same thing: a set with no elements.

Related Ideas

• Zero: The number zero is often thought of as "nothing," similar to how the empty set contains "nothing."

More Information

If you speak Spanish, you can learn more about the empty set here: Conjunto vacío para niños