# 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

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

2021-03-15 19:12:00.328586 UTC