## Abstract

This paper suggests that time could have a much richer mathematical structure than that of the real numbers. Clark & Read (1984) argue that a hypertask (uncountably many tasks done in a finite length of time) cannot be performed. Assuming that time takes values in the real numbers, we give a trivial proof of this. If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an ultratask (a sequence which includes one task done for each ordinal number - thus a proper class of them). We argue that the surreal numbers are in some respects a better model of the temporal continuum than the real numbers as defined in mainstream mathematics, and that surreal time and hypertasks are mathematically possible.

Original language | English (US) |
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Pages (from-to) | 836-847 |

Number of pages | 12 |

Journal | Review of Symbolic Logic |

Volume | 9 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2016 |

### Bibliographical note

Publisher Copyright:Copyright © Association for Symbolic Logic 2016.