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infinity -- infinity

Introduction

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

Related Functions

complexInfinity, undefined

Details

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

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