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Fungrim entry: 04427b

π ⁣(x)=#{p:pPandpx}\pi\!\left(x\right) = \# \left\{ p : p \in \mathbb{P} \,\mathbin{\operatorname{and}}\, p \le x \right\}
Assumptions:xRx \in \mathbb{R}
TeX:
\pi\!\left(x\right) = \# \left\{ p : p \in \mathbb{P} \,\mathbin{\operatorname{and}}\, p \le x \right\}

x \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
PrimePiπ ⁣(x)\pi\!\left(x\right) Prime counting function
Cardinality#S\# S Set cardinality
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
PPP\mathbb{P} Prime numbers
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("04427b"),
    Formula(Equal(PrimePi(x), Cardinality(SetBuilder(p, p, And(Element(p, PP), LessEqual(p, x)))))),
    Variables(x),
    Assumptions(Element(x, RR)))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-17 11:32:46.829430 UTC