Fungrim entry: b738b1

Symbol: Infinity —

\infty

— Positive infinity

This formal symbol represents a quantity larger than any real number. We define

+\infty = \infty

Multiplication of

\infty

by a nonzero complex number represents an infinite limit with the given direction in the complex plane. In particular,

-\infty

i \infty

and

-i \infty

are frequently used.

The set

\mathbb{R} \cup \left\{\infty, -\infty\right\}

is known as the extended real line.

Definitions:

Fungrim symbol	Notation	Short description
`Infinity`	$\infty$	Positive infinity
`ConstI`	$i$	Imaginary unit
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("b738b1"),
    SymbolDefinition(Infinity, Infinity, "Positive infinity"),
    Description("This formal symbol represents a quantity larger than any real number. We define", Equal(Pos(Infinity), Infinity), "."),
    Description("Multiplication of", Infinity, "by a nonzero complex number represents an infinite limit with the given direction in the complex plane.", "In particular,", Neg(Infinity), ",", Mul(ConstI, Infinity), "and", Mul(Neg(ConstI), Infinity), "are frequently used."),
    Description("The set", Union(RR, Set(Infinity, Neg(Infinity))), "is known as the extended real line."))

Topics using this entry

Numbers and infinities