Abstract |

1. | Introduction |

| 1.1 | Why have an infinity? |

| 1.2 | Undefined versus indeterminate; pole |

2. | Orthography |

| 2.1 | Complex complications |

3. | Representation in machine form |

4. | Infinite elements as results; as arguments |

| 4.1 | Infinities as results of monadic scalar functions |

| 4.2 | Infinities as arguments of monadic scalar functions |

| 4.3 | Infinities as results of dyadic scalar functions |

| 4.4 | Infinities as arguments of dyadic scalar functions |

| 4.5 | Infinities as results of mixed functions |

| 4.6 | Infinities as arguments of mixed functions |

5. | Infinite arrays |

| 5.1 | Implementing infinite arrays |

| 5.2 | Scalar functions of infinite arrays |

| 5.3 | Mixed functions of infinite arrays |

| 5.4 | Derived functions of infinite arrays |

| 5.5 | Display of infinite arrays |

| 5.6 | The functions` diag `and` idiag` |

Acknowledgments |

References |