Mathematical texts commonly denote sets by capital letters in italic, such as A, B, C. A set may also be called a … See more

If B is a set and x is an element of B, this is written in shorthand as x ∈ B, which can also be read as "x belongs to B", or "x is in B". The statement "y is not an element of B" is written as y ∉ B, which can also be read as "y is not … See more

The empty set (or null set) is the unique set that has no members. It is denoted ∅, , { }, ϕ, or ϕ. See more

A singleton set is a set with exactly one element; such a set may also be called a unit set. Any such set can be written as {x}, where x is the element. The set {x} and the element x mean different things; Halmos draws the a… See more

If every element of set A is also in B, then A is described as being a subset of B, or contained in B, written A ⊆ B, or B ⊇ A. The latter notation may be read B contains A, B includes A, or B is a superset of A. The … See more

An Euler diagram is a graphical representation of a collection of sets; each set is depicted as a planar region enclosed by a loop, with its elements inside. If A is a subset of B, then the region representing A is complete… See more

There are sets of such mathematical importance, to which mathematicians refer so frequently, that they have acquired special names and notational conventions to identify them.
Many of the… See more