Why is $ \emptyset$ considered a set? My question is short and concise. Here it goes -
In my book the definition of a set is given as a well defined collection of things and in mathematicse they are well defined collection of mathematical objects. Then why is $\emptyset$ which has nothing is even considered as a set. Is it merely a mathematica convention or is it that it has a special significance ? 
Though it is pretty general, I want to know the reason behind it. Thanks for your help .

The existence of the empty set is one of the Zermelo-Frankel axioms of set theory.
One can argue whether or not the concept of the "empty set" violates one's intuition. I can give you an intuitive argument to say that it is not a violation, along the following lines: "Think of a set as the contents of a bag. Just because the bag has no contents doesn't mean it's not a bag."
But that's not the real point, because even if the "empty set" does violate intuition, there is still a good reason to include it in our mathematical language (it often happens that when a mathematical concept is formalized, some of the axioms/rules/concepts that are needed in order for the formalization to work are not as intuitive as one might want; think of the law of logic that says $P \implies Q$ is true whenever the premise $P$ is false and the conclusion $Q$ is true). 
What's the reason? Among other possible reasons, one can say that similar to how the theory of addition is simpler when one introduces zero, the theory of sets is simpler when one introduces the emptyset. One wants to be able to define the binary operation of intersection $A \cap B$ for all pairs of sets $A$ and $B$. The definition is:
$$A \cap B = \{x \bigm| \text{$x \in A$ and $x \in B$}\}
$$
However, what if there does not exist any $x$ such that $x \in A$ and $x \in B$? In that case, the only candidate for $A \cap B$ is the empty set, so if the empty set does not exist then $A \cap B$ is not always defined.
