## `infinity` -- infinity

#### Introduction

`infinity` represents the infinite point on the positive real semi-axis.

#### Related Functions

`complexInfinity`, `undefined`

#### Details

- `infinity` is an element of the domain `stdlib::Infinity`. It may be used in arithmetical operations. Some system functions accept `infinity` as a parameter or return it as a result.

#### Example 1

`infinity` can be used in arithmetical operations with real numbers:

    >> 7*infinity + 3, -3.0*infinity, 1/infinity,
       infinity*infinity, infinity^2, sqrt(infinity)

               infinity, -infinity, 0, infinity, infinity, infinity

Arithmetic with complex numbers or symbolic objects yields symbolic expressions:

    >> I*infinity + b

                                  b + I infinity

The arithmetic responds to properties:

    >> assume(a > 0): a*infinity

                                     infinity

    >> assume(a < 0): a*infinity

                                     -infinity

    >> unassume(a): a*infinity

                                    a infinity

Cancellation of infinities yields `undefined`:

    >> infinity - infinity, infinity/infinity

                               undefined, undefined

Some system functions accept `infinity` as a parameter or return it as result:

    >> exp(infinity), sum(1/n, n = 1..infinity),
       int(exp(-x^2), x = -infinity..infinity),
       limit(x, x = infinity)

                                              1/2
                        infinity, infinity, PI   , infinity

#### Changes

- no changes

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