Sets are fundamental objects in mathematics. Intuitively, a set is merely a collection of elements or members. There are various conventions for textually denoting sets. In any particular situation, an author typically chooses from among these conventions depending on which properties of the set are most relevant to the immediate context or on which perspective is most useful.

Denoting a set as an object

Where it is desirable to refer to a set as an indivisible entity, one typically denotes it by a single capital letter. In referring to an arbitrary, generic set, a typical notational choice is S. When several sets are being discussed simultaneously, they are often denoted by the first few capitals: A, B, C, and so forth. As another example, there is a nearly universal notational convention that covers certain very important sets of numbers as follows:

Some authors use the blackboard bold font for these particular sets (, , etc.). This usage is widely accepted in handwriting, but many mathematicians, and such experts on mathematical typography as Donald Knuth, advise against its use in print.

Another single-character symbol for a set is , which is very widely used to denote the empty set.