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."))