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The empty set is the set with no elements. It's commonly written as either $\emptyset$, $\varnothing$, or $\{\}$.

Do you think the empty set should count as a set?

Mathematicians generally agree that the empty set should count as a set, not out of philosophical conviction but out of convenience.

For example, let's say we're asking for the solutions of a certain equation of the form $ax^{2} + bx + c = 0$. What kind of answer are we expecting? Not just a number, since there might not be exactly one solution.

We're expecting a set of solutions, like $\{2\}$ or $\{-1, 4\}$. But what if there are no solutions? In this case, it would be nice to still be able to describe the solutions as a set. So here the empty set comes into play; the solution set would be $\varnothing$.

Because of the empty set, we can talk about the "solution set" of an equation without fear that it might not exist. This is just one of many examples in which the empty set is convenient to have around!

An empty set is a set which does not have any elements to be listed. In other words, it is empty. An empty set is represented by $\emptyset$ or $\{\}$.

Empty set is very useful in defining some characteristics of certain sets, and some important results in set theory.

Examples:

1. Set of natural numbers smaller than 1.

2. Intersection of any two disjoint sets.

3. Set of even numbers between 4 and 6.

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