There are a number of sets that come up frequently in discussions and so have special names.

The empty set

The empty set is the set with no members, usually notated either \(\{ \}\) or \(\emptyset\). 

There's only one empty set, since two empty sets would have the same elements and therefore be the same set.  So while you can have many different arrays of zero length in a program, there's only one empty set.

Sets of numbers

The sets of different types of numbers come up frequently:

• The set of natural numbers: \(\{ 0, 1, 2, ... \}\).  These are often referred to by the name \(\mathbb N\).
• The integers: \(\{ ..., -2, -1, 0, 1, 2, ... \}\).  These are often referred to by the name \(\mathbb Z\).  Why Z?  Because it stands for zahl, which is German for “number”.
• The rational numbers, \(\mathbb Q\), which are all the fractions.  Why Q?  Because we want to use R for the reals, and Q stands for “quotient”, i.e. division.
• The real numbers, \(\mathbb R\).