Fungrim symbol: PrimePi

Symbol: PrimePi —

\pi(x)

— Prime counting function

Domain	Codomain
$x \in \mathbb{R}$	$\pi(x) \in \mathbb{Z}_{\ge 0}$
$x \in \left\{\infty\right\}$	$\pi(x) \in \left\{\infty\right\}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \;\implies\; \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`PrimePi`	$\pi(x)$	Prime counting function
`RR`	$\mathbb{R}$	Real numbers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("6c22c8"),
    SymbolDefinition(PrimePi, PrimePi(x), "Prime counting function"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(x, RR), Element(PrimePi(x), ZZGreaterEqual(0))), Tuple(Element(x, Set(Infinity)), Element(PrimePi(x), Set(Infinity))))))

Topics using this symbol

The symbol PrimePi appears in 3 topics:

Prime numbers (in 8 entries)
Riemann hypothesis (in 2 entries)
Integer sequences (in 1 entries)

Entries using this symbol

The symbol PrimePi appears in 9 entries: