## Provability, Computability and ReflectionProvability, Computability and Reflection |

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### Contents

1 | |

Chapter II Recursive and Relative Continuity | 39 |

Chapter III Recursive and Relative Differentiability | 57 |

Chapter IV The Relative Integral | 87 |

Chapter V The Elementary Functions | 96 |

### Common terms and phrases

arcsin aſm aſn completes the proof converges recursively cos(n decision procedure define denote e-number effectively constant effectively variable equivalent recursive real equivalent to f(n f(k+ fg(k fg(n fi(n fl(m fl(n greatest integer Hence hypothesis If(n induction inverse functions Let f(n majorant n mean value theorem natural numbers ºff ºwn polynomial primitive recursive function primitive recursive real procedure for deciding propositional calculus proves that f(n real number f(n recursive analysis recursive arithmetic recursive cº recursive function f(n recursive real number recursively divergent recursively irrational recursively to zero relative convergence relative to n relatively continuous function relatively differentiable relatively integrable relatively variable Rolle's theorem Rolle’s ruled function satisfying sequence of ordinals shows Similarly sin(n standard form taking Taylor's theorem tends recursively tetration transfinite induction uniform Rolle's theorem uniformly convergent uniformly recursively convergent whence it follows write