*Divergence: What to Do Till the Mathematician Comes*

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Scientific Paper | |
---|---|

Title | Divergence: What to Do Till the Mathematician Comes |

Author(s) | Thomas E Phipps |

Keywords | divergence, divergent series, mathematics, definitions, convergence, infinite series, summability, terminal summation, Brown's function, Brown's series, Euler |

Published | 2001 |

Journal | Physics Essays |

Volume | 14 |

Number | 4 |

Pages | 341-353 |

## Abstract

It is argued that definitions may be chosen a posteriori to reflect mathematical existence?the opposite of the usual approach by which definitions are chosen a priori and used to prove existence. This inverted view is applied to the question of ?divergence.? It is shown that a definition employing approximations to process remainders known as ?terminal summation? allows ?values? of divergent series to exist.