Phrase | Definition |

a priori | A fact is known 'a priori' if it is evident from logic alone, without need of evidence. |

ad hoc | For this purpose |

ad infinitum | To infinity, usually referring to a never ending process. |

Ansatz | An educated guess that is not rigourously backed up. |

cf. confer | Compare |

Conjecture | A result that is thought to be true but no proof exists. |

Corollary | A smaller result that is a consequence from a larger theorem. |

e.g. exempli gratia | For example |

ergo | Therefore |

errata | Errors, usually referring to a list of corrections made since the last edition. |

et al. et alia | And others |

etc. et cetera | And so on |

Hypothesis | A proposal consistent with known data and not shown to be true or false. |

i.e. id est | That is |

ibid. ibidem | The same place. Usually means the reference being used is the same as the previous one. |

iff if and only if | The preceding and subsequent statements are equivalent. |

L.H.S. Left Hand Side | Refers to the left side of the equality in an equation and similar for inequalities etc. |

Lemma | A statement and proof, relatively unimportant in their own right usually given in work towards a more substantial result such as a theorem. |

modus ponendo tollens | If both statements A and B can't be true, and we know that A is true, we know that B is false. |

modus ponens | If statement A implies B, and we know that A is true, then B is also true. |

modus tollens | If statement A implies statement B and we know that statement B is false, then A is false. |

n.b. nota bene | Note well |

Q.E.D. quod erat demonstrandum | That which was to be proved. Given at the end of a proof. |

Q.E.F. quod erat faciendum | That which was to be shown. Given at the end of a calculation. |

R.H.S. Right Hand Side | Refers to the right side of the equality in an equation and similar for inequalities etc. |

reductio ad absurdum | Reduction to absurdity. "This implies an absurtity and so is false." Proof by contradiction. |

s.t. such that | such that |

Theorem | A statement that has been proven from already established facts. |

w.l.o.g. without loss of generality | An argument is to be used for a specific case, which is easily applied to the others. |

w.r.t. with respect to | Referring to |