Fungrim symbol: Cardinality

Symbol: Cardinality —

\# S

— Set cardinality

Cardinality(S), rendered as

\# S

, represents the cardinality of the set

S

. The cardinality of a finite set is a nonnegative integer. Cardinalities of infinite sets may be represented in terms of this symbol; for example,

\# \mathbb{Z}

is the cardinality of any countable set and

\# \mathbb{R}

is the cardinality of the continuum.

Definitions:

Fungrim symbol	Notation	Short description
`Cardinality`	$\# S$	Set cardinality
`ZZ`	$\mathbb{Z}$	Integers
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("81efd5"),
    SymbolDefinition(Cardinality, Cardinality(S), "Set cardinality"),
    Description(SourceForm(Cardinality(S)), ", rendered as", Cardinality(S), ", represents the cardinality of the set", S, ".", "The cardinality of a finite set is a nonnegative integer.", "Cardinalities of infinite sets may be represented in terms of this symbol;", "for example,", Cardinality(ZZ), "is the cardinality of any countable set", "and", Cardinality(RR), "is the cardinality of the continuum."))

Topics using this symbol

The symbol Cardinality appears in 11 topics:

Dirichlet characters (in 7 entries)
Partition function (in 5 entries)
Greatest common divisor (in 4 entries)
Bell numbers (in 4 entries)
Totient function (in 2 entries)
Prime numbers (in 1 entries)
Modular j-invariant (in 1 entries)
Legendre polynomials (in 1 entries)
Fibonacci numbers (in 1 entries)
Elementary logic and set theory (in 1 entries)
Eisenstein series (in 1 entries)

Entries using this symbol

The symbol Cardinality appears in 28 entries: