Set notation

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.

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. By convention, particular symbols are reserved for the most important sets of numbers:

Some authors use the blackboard bold font for these particular sets (${\displaystyle \mathbb {C} }$, ${\displaystyle \mathbb {N} }$, 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.

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